{
"cells": [
{
"cell_type": "markdown",
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"source": [
"# Basic trigonometry\n",
"\n",
"> Marcos Duarte \n",
"> Laboratory of Biomechanics and Motor Control ([http://demotu.org/](http://demotu.org/)) \n",
"> Federal University of ABC, Brazil"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If two right triangles (triangles with an angle of $90^o$ ($\\pi/2$ radians)) have equal acute angles, they are similar, so their side lengths are proportional. \n",
"These proportionality constants are the values of $\\sin\\theta$, $\\cos\\theta$, and $\\tan\\theta$. \n",
"Here is a geometric representation of the main [trigonometric functions](http://en.wikipedia.org/wiki/Trigonometric_function) of an angle $\\theta$: \n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Radian\n",
"\n",
"An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian: \n",
"
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Common trigonometric values\n",
"\n",
"
$\\;\\theta\\;(^o)$ | \n", "$\\;\\theta\\;(rad)$ | \n", "$\\;\\sin \\theta\\;$ | \n", "$\\;\\cos \\theta\\;$ | \n", "$\\;\\tan \\theta\\;$ | \n", "
---|---|---|---|---|
$0^o$ | \n", "$0$ | \n", "$0$ | \n", "$1$ | \n", "$0$ | \n", "
$30^o$ | \n", "$\\pi/6$ | \n", "$1/2$ | \n", "$\\sqrt{3}/2$ | \n", "$1\\sqrt{3}$ | \n", "
$45^o$ | \n", "$\\pi/4$ | \n", "$\\sqrt{2}/2$ | \n", "$\\sqrt{2}/2$ | \n", "$1$ | \n", "
$60^o$ | \n", "$\\pi/3$ | \n", "$\\sqrt{3}/2$ | \n", "$1/2$ | \n", "$\\sqrt{3}$ | \n", "
$90^o$ | \n", "$\\pi/2$ | \n", "$1$ | \n", "$0$ | \n", "$\\infty$ | \n", "