TRIGONOMETRIC_FUNCTIONS
The C++ program featured in this tutorial web page defines the following nine trigonometric functions (whose inputs are each some angle measurement, x, in radians ): sine(x), cosine(x), tangent(x), cotangent(x), secant(x), cosecant(x), arctangent(x), arcsine(x), arccosine(x).
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SOFTWARE_APPLICATION_COMPONENTS
C++_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_23/main/trigonometric_functions.cpp
plain-text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_23/main/trigonometric_functions_output.txt
PROGRAM_COMPILATION_AND_EXECUTION
STEP_0: Copy and paste the C++ source code into a new text editor document and save that document as the following file name:
trigonometric_functions.cpp
STEP_1: Open a Unix command line terminal application and set the current directory to wherever the C++ program file is located on the local machine (e.g. Desktop).
cd Desktop
STEP_2: Compile the C++ file into machine-executable instructions (i.e. object file) and then into an executable piece of software named app using the following command:
g++ trigonometric_functions.cpp -o app
STEP_3: If the program compilation command does not work, then use the following commands (in top-down order) to install the C/C++ compiler (which is part of the GNU Compiler Collection (GCC)):
sudo apt install build-essential
sudo apt-get install g++
STEP_4: After running the g++ command, run the executable file using the following command:
./app
STEP_5: Once the application is running, the following prompt will appear:
Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000:
STEP_6: Enter a value for x using the keyboard. Proceed with the prompts for additional input values which follow.
STEP_7: Observe program results on the command line terminal and in the output file.
PROGRAM_SOURCE_CODE
The text in the preformatted text box below appears on this web page (while rendered correctly by the web browser) to be identical to the content of the C++ source code file whose Uniform Resource Locator is displayed in the green hyperlink below. A computer interprets that C++ source code as a series of programmatic instructions (i.e. software) which govern how the hardware of that computer behaves.
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C++_source_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_23/main/trigonometric_functions.cpp
/**
* file: trigonometric_functions.cpp
* type: C++ (source file)
* date: 18_OCTOBER_2024
* author: karbytes
* license: PUBLIC_DOMAIN
*/
/** preprocessing directives */
#include <iostream> // standard input (std::cin), standard output (std::cout)
#include <fstream> // file input, file output
#define MAXIMUM_i 10000 // constant which represents maximum number of iterations in Leibniz series
#define MAXIMUM_t 10000 // constant which represents maximum number of terms in Taylor series
#define MAXIMUM_x 10000 // constant which represents maximum value of x
/** function prototypes */
double computePi(int iterations);
double sine(double x);
double cosine(double x);
double tangent(double x);
double cotangent(double x);
double secant(double x);
double cosecant(double x);
double arctangent(double x);
double arcsine(double x);
double arccosine(double x);
/** program entry point */
int main()
{
// Define one double type variable for storing a floating-point number value.
double x;
// Declare a variable for storing the program user's answer of whether or not to continue inputting values.
int input_additional_values = 1;
// Declare a file output stream handler (which represents the plain-text file to generate and/or overwrite with program data).
std::ofstream file;
// Set the number of digits of floating-point numbers which are printed to the command line terminal to 100 digits.
std::cout.precision(100);
// Set the number of digits of floating-point numbers which are printed to the file output stream to 100 digits.
file.precision(100);
/**
* If the file named trigonometric_functions_output.txt does not already exist
* inside of the same file directory as the file named trigonometric_functions.cpp,
* create a new file named trigonometric_functions_output.txt in that directory.
*
* Open the plain-text file named trigonometric_functions_output.txt
* and set that file to be overwritten with program data.
*/
file.open("trigonometric_functions_output.txt");
// Print an opening message to the command line terminal.
std::cout << "\n\n--------------------------------";
std::cout << "\nStart Of Program";
std::cout << "\n--------------------------------";
// Print an opening message to the file output stream.
file << "--------------------------------";
file << "\nStart Of Program";
file << "\n--------------------------------";
// Print "This C++ program computes sine, cosine, tangent, cotangent, secant, cosecant, arctangent, arcsine, and arccosine of some angle measurement in radians, x.
std::cout << "\n\nThis C++ program computes sine, cosine, tangent, cotangent, secant, cosecant, arctangent, arcsine, and arccosine of some angle measurement in radians, x.";
file << "\n\nThis C++ program computes sine, cosine, tangent, cotangent, secant, cosecant, arctangent, arcsine, and arccosine of some angle measurement in radians, x.";
// Execute the code inside of the while loop block at least once (and until the program user inputs a value specifying to exit the program).
while (input_additional_values != 0)
{
// Print a horizontal divider line to the command line terminal and to the file output stream.
std::cout << "\n\n--------------------------------";
file << "\n\n--------------------------------";
// Prompt the user to enter an input value for x (and print that prompt to the command line terminal and to the file output stream).
std::cout << "\n\nEnter a real number of radians, x, to input into trigonometric functions which is no smaller than " << (-1 * MAXIMUM_x) << " and no larger than " << MAXIMUM_x << ": ";
file << "\n\nEnter a real number of radians, x, to input into trigonometric functions which is no smaller than " << (-1 * MAXIMUM_x) << " and no larger than " << MAXIMUM_x << ": ";
// Scan the command line terminal for the most recent keyboard input value. Store that value in x.
std::cin >> x;
// Print "The value which was entered for x is {x}." to the command line terminal and to the file output stream.
std::cout << "\nThe value which was entered for x is " << x << ".";
file << "\n\nThe value which was entered for x is " << x << ".";
// Print a horizontal divider line to the command line terminal and to the file output stream.
std::cout << "\n\n--------------------------------";
file << "\n\n--------------------------------";
// Print the value of sine of x to the command line terminal and to the output file.
std::cout << "\n\nsine(x) = " << sine(x) << ".";
file << "\n\nsine(x) = " << sine(x) << ".";
// Print the value of cosine of x to the command line terminal and to the output file.
std::cout << "\n\ncosine(x) = " << cosine(x) << ".";
file << "\n\ncosine(x) = " << cosine(x) << ".";
// Print the value of tangent of x to the command line terminal and to the output file.
std::cout << "\n\ntangent(x) = " << tangent(x) << ".";
file << "\n\ntangent(x) = " << tangent(x) << ".";
// Print a horizontal divider line to the command line terminal and to the file output stream.
std::cout << "\n\n--------------------------------";
file << "\n\n--------------------------------";
// Print the value of cotangent of x to the command line terminal and to the output file.
std::cout << "\n\ncotangent(x) = " << cotangent(x) << ".";
file << "\n\ncotangent(x) = " << cotangent(x) << ".";
// Print the value of secant of x to the command line terminal and to the output file.
std::cout << "\n\nsecant(x) = " << secant(x) << ".";
file << "\n\nsecant(x) = " << secant(x) << ".";
// Print the value of cosecant of x to the command line terminal and to the output file.
std::cout << "\n\ncosecant(x) = " << secant(x) << ".";
file << "\n\ncosecant(x) = " << secant(x) << ".";
// Print a horizontal divider line to the command line terminal and to the file output stream.
std::cout << "\n\n--------------------------------";
file << "\n\n--------------------------------";
// Print the value of arctangent of x to the command line terminal and to the output file.
std::cout << "\n\narctangent(x) = " << arctangent(x) << ".";
file << "\n\narctangent(x) = " << arctangent(x) << ".";
// Print the value of arcsine of x to the command line terminal and to the output file.
std::cout << "\n\narcsine(x) = " << arcsine(x) << ".";
file << "\n\narcsine(x) = " << arcsine(x) << ".";
// Print the value of arccosine of x to the command line terminal and to the output file.
std::cout << "\n\narccosine(x) = " << arccosine(x) << ".";
file << "\n\narccosine(x) = " << arccosine(x) << ".";
// Print a horizontal divider line to the command line terminal and to the file output stream.
std::cout << "\n\n--------------------------------";
file << "\n\n--------------------------------";
// Ask the user whether or not to continue inputing values.
std::cout << "\n\nWould you like to continue inputting program values? (Enter 1 if YES. Enter 0 if NO): ";
// Scan the command line terminal for the most recent keyboard input value.
std::cin >> input_additional_values;
}
// Print a closing message to the command line terminal.
std::cout << "\n\n--------------------------------";
std::cout << "\nEnd Of Program";
std::cout << "\n--------------------------------\n\n";
// Print a closing message to the file output stream.
file << "\n\n--------------------------------";
file << "\nEnd Of Program";
file << "\n--------------------------------";
// Close the file output stream.
file.close();
// Exit the program.
return 0;
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function computes the approximate value of Pi using the Leibniz series.
*
* Pi ≈ 4 * (1 - (1 / 3) + (1 / 5) - (1 / 7) + (1 / 9) - ...)
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* Pi is a mathematical constant that is the ratio of a circle's circumference to
* its diameter (which is approximately equal to 3.14159).
*
* For more information on how to compute the approximate value of Pi
* (using a Monte Carlo dart-throwing simulation in JavaScript), visit
* the tutorial web page at the following Uniform Resource Locator:
*
* https://karlinaobject.wordpress.com/pi_approximation/
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* iterations is assumed to be a nonnegative integer no larger than MAXIMUM_iteratons.
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double computePi(int iterations)
{
int i = 0;
double pi = 0.0;
double sign = 1.0; // alternates between positive and negative
// Set iterations to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((iterations < 0) || (iterations > MAXIMUM_i))
{
iterations = 1;
std::cout << "\n\nThe number of iterations for the Leibniz series in computePi(iterations) was out of range. Hence, iterations has been reset to 1.";
}
for (i = 0; i < iterations; i += 1)
{
pi += sign / (2.0 * i + 1.0); // add next term in the series
sign = -sign; // alternate the sign for each term
}
pi *= 4.0; // multiply by 4 to get Pi
return pi;
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function uses the Taylor series to compute the approximate value of sine of x (which is also expressed as sin(x)).
*
* The value returned by this function is no smaller than -1 and no larger than 1:
*
* -1 <= sin(x) <= 1
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The sine of an angle, x, in a right triangle is defined as the ratio of the length of
* the side opposite the angle to the length of the hypotenuse (the longest side of the triangle):
*
* sin(x) = opposite / hypotenuse
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* Note that an angle measurement in degrees can be converted to radians using the following formula:
*
* radians = degrees * (Pi / 180)
*
* If x is 30 degrees, then the right triangle it is the interior angle measurement of is a triangle
* whose side opposite of x is 1 and whose hypotenuse is 2.
*
* Hence, sine of 30 degrees can be computed as follows:
*
* 30 degrees = Pi / 6 radians ≈ 0.5236
*
* sin(0.5236) = 1 / 2 = 0.5
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians and can theoretically be any real number (but is constrained to be in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double sine(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in sine(x) was out of range. Hence, x has been reset to 1.";
}
int i = 0;
const int terms = MAXIMUM_t; // number of terms in the Taylor series
double result = 0.0;
double term = x; // first term: ((x ^ 1) / 1!)
int sign = 1; // alternating signs for each term
for (i = 1; i <= terms; i += 1)
{
result += sign * term;
sign *= -1; // alternating sign
term *= x * x / (2 * i * (2 * i + 1)); // update term for the next iteration
}
return result;
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function uses the Taylor series to compute the approximate value of cosine of x (which is also expressed as cos(x)).
*
* The value returned by this function is no smaller than -1 and no larger than 1:
*
* -1 <= cos(x) <= 1
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The cosine of an angle, x, in a right triangle is defined as the ratio of the length of
* the side adjacent to the angle to the length of the hypotenuse (the longest side of the triangle):
*
* cos(x) = adjacent / hypotenuse
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* Note that an angle measurement in degrees can be converted to radians using the following formula:
*
* radians = degrees * (Pi / 180)
*
* If x is 60 degrees, then the right triangle it is the interior angle measurement of is a triangle
* whose side adjacent to x is 1 and whose hypotenuse is 2.
*
* Hence, cosine of 60 degrees can be computed as follows:
*
* 60 degrees = Pi / 3 radians ≈ 1.047
*
* cos(1.047) = 1 / 2 = 0.5
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians and can theoretically be any real number (but is constrained to be in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double cosine(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in cosine(x) was out of range. Hence, x has been reset to 1.";
}
int i = 0;
const int terms = MAXIMUM_t; // number of terms in the Taylor series
double result = 1.0; // first term: ((x ^ 0) / 0!)
double term = 1.0;
int sign = -1; // alternating signs for each term
for (i = 1; i <= terms; i += 1)
{
term *= x * x / (2 * i * (2 * i - 1)); // update term for the next iteration
result += sign * term;
sign *= -1; // alternating sign
}
return result;
}
/**
*-----------------------------------------------------------------------------------------------------------------------------------
*
* This function computes the approximate value of tangent of x (which is also expressed as tan(x)).
*
* The value returned by this function can theoretically be any real number:
*
* tan(x) ∈ (-INFINITY, INFINITY)
*
*-----------------------------------------------------------------------------------------------------------------------------------
*
* The tangent of an angle, x, in a right triangle is defined as the ratio of the length of the side opposite
* the angle to the length of the adjacent side:
*
* tan(x) = opposite / adjacent
*
*-----------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians such that, theoretically speaking,
*
* x = (((2 * n) + 1) * Pi) / 2
*
* where n is any integer
*
* (but, in this program function, x is allowed to be any integer in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is within [(-1 * MAXIMUM_x), MAXIMUM_x] but
*
* x != (((2 * n) + 1) * Pi) / 2
*
* where n is theoretically any integer,
*
* then the output value returned by this function will be "not a number".
*
* For example, if x = Pi /2, then tan(x) = "not a number".
*
*-----------------------------------------------------------------------------------------------------------------------------------
*/
double tangent(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in tangent(x) was out of range. Hence, x has been reset to 1.";
}
return sine(x) / cosine(x);
}
/**
*-----------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the reciprocal of the tangent function:
*
* cotangent(x) = cot(x) = 1 / tan(x)
*
*------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number:
*
* cot(x) ∈ (-INFINITY, INFINITY)
*
*------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians such that, theoretically speaking,
*
* sin(x) != 0
*
* (i.e.
*
* x != (Pi * n)
*
* where n is any integer)
*
* (but, in this program function, x is allowed to be any integer in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is within [(-1 * MAXIMUM_x), MAXIMUM_x] but also
*
* x = Pi * n
*
* where n is any integer
*
* then the output value returned by this function will be "not a number".
*
* For example, if x = Pi, then cot(x) = "not a number".
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double cotangent(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in cotangent(x) was out of range. Hence, x has been reset to 1.";
}
return 1.0 / tangent(x);
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the reciprocal of the cosine function:
*
* secant(x) = sec(x) = 1 / cos(x)
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number less than or equal to -1
* or else any real number greater than or equal to 1:
*
* sec(x) ∈ (-INFINITY, -1] ∪ [1, INFINITY)
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians such that, theoretically speaking,
*
* cos(x) != 0
*
* (i.e.
*
* x != (((2 * n) + 1) * Pi) / 2
*
* where n is any integer)
*
* (but, in this program function, x is allowed to be any integer in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is within [(-1 * MAXIMUM_x), MAXIMUM_x] but also
*
* x = (((2 * n) + 1) * Pi) / 2
*
* where n is any integer
*
* then the output value returned by this function will be "not a number".
*
* For example, if x = Pi / 2, then cot(x) = "not a number".
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double secant(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in secant(x) was out of range. Hence, x has been reset to 1.";
}
return 1.0 / cosine(x);
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the reciprocal of the sine function:
*
* cosecant(x) = cos(x) = 1 / sin(x)
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number less than or equal to -1
* or else any real number greater than or equal to 1:
*
* csc(x) ∈ (-INFINITY, -1] ∪ [1, INFINITY)
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians such that, theoretically speaking,
*
* sin(x) != 0
*
* (i.e.
*
* x != (Pi * n)
*
* where n is any integer)
*
* (but, in this program function, x is allowed to be any integer in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is within [(-1 * MAXIMUM_x), MAXIMUM_x] but also
*
* x = Pi * n
*
* where n is any integer
*
* then the output value returned by this function will be "not a number".
*
* For example, if x = Pi, then csc(x) = "not a number".
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double cosecant(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in cosecant(x) was out of range. Hence, x has been reset to 1.";
}
return 1.0 / sine(x);
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the inverse of the cosine function using the Taylor series:
*
* arctangent(x) = atan(x) = tan ^ -1 (x) != 1 / tan(x) = (tan(x)) ^ -1
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number less than or equal to (-1 * (Pi / 2))
* or any real number greater than or equal to (Pi / 2):
*
* atan(x) ∈ [(-1 * (Pi / 2)), (Pi / 2)]
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians and can theoretically be any real number (but is constrained to be in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double arctangent(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in arctangent(x) was out of range. Hence, x has been reset to 1.";
}
int i = 0;
const int terms = MAXIMUM_t; // number of terms in the series
double result = 0.0;
double term = x; // first term
int sign = 1; // alternating signs for each term
for (i = 0; i < terms; i += 1)
{
result += sign * term;
sign *= -1; // alternating sign
term *= x * x * (2 * i + 1) / (2 * i + 3); // update term for the next iteration
}
return result;
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the inverse of the sine function using the Taylor series:
*
* arcsine(x) = asin(x) = sin ^ -1 (x) != 1 / sin(x) = (sin(x)) ^ -1
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number less than or equal to (-1 * (Pi / 2))
* or any real number greater than or equal to (Pi / 2):
*
* asin(x) ∈ [(-1 * (Pi / 2)), (Pi / 2)]
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians and is only valid if
*
* x ∈ [-1, 1]
*
* where x is a real number
*
* (but, in this program, x can be in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is out of range of [-1, 1], then asin(x) = "not a number".
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double arcsine(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in arcsine(x) was out of range. Hence, x has been reset to 1.";
}
const int terms = MAXIMUM_t;
double result = x;
double term = x;
for (int i = 1; i < terms; ++i)
{
term *= (x * x * (2 * i - 1)) / (2 * i);
result += term / (2 * i + 1);
}
return result;
}
/**
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* This function returns the inverse of the cosine function using the following formula: acos(x) = pi/2 - asin(x)
*
* arccosine(x) = acos(x) = cos ^ -1 (x) != 1 / cos(x) = (cos(x)) ^ -1
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* The value returned by this function can theoretically be any real number less than or equal to 0
* or any real number greater than or equal to Pi:
*
* acos(x) ∈ [0, Pi]
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*
* x is an angle measurement in radians and is only valid if
*
* x ∈ [-1, 1]
*
* where x is a real number
*
* (but, in this program, x can be in [(-1 * MAXIMUM_x), MAXIMUM_x]).
*
* If x is out of range of [-1, 1], then acos(x) = "not a number".
*
*----------------------------------------------------------------------------------------------------------------------------------------------
*/
double arccosine(double x)
{
// Set x to 1 if the function input value is out or range. Then print a message about that change to the command line terminal.
if ((x < (-1 * MAXIMUM_x)) || (x > MAXIMUM_x))
{
x = 1;
std::cout << "\n\nThe number of radians, x, in arccosine(x) was out of range. Hence, x has been reset to 1.";
}
return computePi(MAXIMUM_i) / 2 - arcsine(x);
}
SAMPLE_PROGRAM_OUTPUT
The text in the preformatted text box below was generated by one use case of the C++ program featured in this computer programming tutorial web page.
plain-text_file: https://raw.githubusercontent.com/karlinarayberinger/KARLINA_OBJECT_extension_pack_23/main/trigonometric_functions_output.txt
-------------------------------- Start Of Program -------------------------------- This C++ program computes sine, cosine, tangent, cotangent, secant, cosecant, arctangent, arcsine, and arccosine of some angle measurement in radians, x. -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is 0.25. -------------------------------- sine(x) = 0.2474039592545229371278736607564496807754039764404296875. cosine(x) = 0.96891242171064473343022882545483298599720001220703125. tangent(x) = 0.25534192122103627209384058005525730550289154052734375. -------------------------------- cotangent(x) = 3.916317364645939935741125736967660486698150634765625. secant(x) = 1.0320850239843857298893681218032725155353546142578125. cosecant(x) = 1.0320850239843857298893681218032725155353546142578125. -------------------------------- arctangent(x) = 0.2449786631268640879621756312189972959458827972412109375. arcsine(x) = 0.252680255142078646901637739574653096497058868408203125. arccosine(x) = 1.31806607165293865335797818261198699474334716796875. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is 9. -------------------------------- sine(x) = 0.41211848524176553087983165823970921337604522705078125. cosine(x) = -0.911130261884733894106602747342549264430999755859375. tangent(x) = -0.45231565944179141780523423221893608570098876953125. -------------------------------- cotangent(x) = -2.2108454109992852210098135401494801044464111328125. secant(x) = -1.097537906304893340347916819155216217041015625. cosecant(x) = -1.097537906304893340347916819155216217041015625. -------------------------------- arctangent(x) = -nan. arcsine(x) = inf. arccosine(x) = -inf. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is 3.14158999999999988261834005243144929409027099609375. -------------------------------- sine(x) = 2.65358979382669020406749181562044981319559155963361263275146484375e-06. cosine(x) = -0.999999999996479704833518553641624748706817626953125. tangent(x) = -2.653589793836031706926285866909864807894336991012096405029296875e-06. -------------------------------- cotangent(x) = -376847.9975024320301599800586700439453125. secant(x) = -1.000000000003520295166481446358375251293182373046875. cosecant(x) = -1.000000000003520295166481446358375251293182373046875. -------------------------------- arctangent(x) = -nan. arcsine(x) = inf. arccosine(x) = -inf. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is 0.52359999999999995434762922741356305778026580810546875. -------------------------------- sine(x) = 0.50000106036260294484208088761079125106334686279296875. cosine(x) = 0.8660247915829388798414356642751954495906829833984375. tangent(x) = 0.5773519017263815111817848446662537753582000732421875. -------------------------------- cotangent(x) = 1.7320459099724587748170279155601747334003448486328125. secant(x) = 1.1547013546484949930714947186061181128025054931640625. cosecant(x) = 1.1547013546484949930714947186061181128025054931640625. -------------------------------- arctangent(x) = 0.482348868051956036762106805326766334474086761474609375. arcsine(x) = 0.55107102025035559211829649939318187534809112548828125. arccosine(x) = 1.019675306544661541607865729019977152347564697265625. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is 0. -------------------------------- sine(x) = 0. cosine(x) = 1. tangent(x) = 0. -------------------------------- cotangent(x) = inf. secant(x) = 1. cosecant(x) = 1. -------------------------------- arctangent(x) = 0. arcsine(x) = 0. arccosine(x) = 1.5707463267950172447484646909288130700588226318359375. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is -1. -------------------------------- sine(x) = -0.8414709848078965048756572286947630345821380615234375. cosine(x) = 0.54030230586813965398818027097149752080440521240234375. tangent(x) = -1.5574077246549025144162214928655885159969329833984375. -------------------------------- cotangent(x) = -0.642092615934330535054641586611978709697723388671875. secant(x) = 1.8508157176809258981364791907253675162792205810546875. cosecant(x) = 1.8508157176809258981364791907253675162792205810546875. -------------------------------- arctangent(x) = -0.78537316339750928850804712055833078920841217041015625. arcsine(x) = -1.56515440745319533988322291406802833080291748046875. arccosine(x) = 3.13590073424821280667629253002814948558807373046875. -------------------------------- -------------------------------- Enter a real number of radians, x, to input into trigonometric functions which is no smaller than -10000 and no larger than 10000: The value which was entered for x is -0.01000000000000000020816681711721685132943093776702880859375. -------------------------------- sine(x) = -0.00999983333416666446413767488365920144133269786834716796875. cosine(x) = 0.9999500004166652633585954390582628548145294189453125. tangent(x) = -0.0100003333466672054974377914504657383076846599578857421875. -------------------------------- cotangent(x) = -99.99666664444424668545252643525600433349609375. secant(x) = 1.0000500020834179881745740203768946230411529541015625. cosecant(x) = 1.0000500020834179881745740203768946230411529541015625. -------------------------------- arctangent(x) = -0.00999966668666523762765141469799345941282808780670166015625. arcsine(x) = -0.01000016667416711406424223440581044997088611125946044921875. arccosine(x) = 1.5807464934691843883030060169403441250324249267578125. -------------------------------- -------------------------------- End Of Program --------------------------------
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