#!/usr/bin/env python
# coding: utf-8
# # Basic trigonometry
#
# > Marcos Duarte
# > Laboratory of Biomechanics and Motor Control ([http://demotu.org/](http://demotu.org/))
# > Federal University of ABC, Brazil
# 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.
# These proportionality constants are the values of $\sin\theta$, $\cos\theta$, and $\tan\theta$.
# Here is a geometric representation of the main [trigonometric functions](http://en.wikipedia.org/wiki/Trigonometric_function) of an angle $\theta$:
#
#
# ## Radian
#
# An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian:
#
#
# ## Common trigonometric values
#
#
$\;\theta\;(^o)$ | #$\;\theta\;(rad)$ | #$\;\sin \theta\;$ | #$\;\cos \theta\;$ | #$\;\tan \theta\;$ | #
---|---|---|---|---|
$0^o$ | #$0$ | #$0$ | #$1$ | #$0$ | #
$30^o$ | #$\pi/6$ | #$1/2$ | #$\sqrt{3}/2$ | #$1\sqrt{3}$ | #
$45^o$ | #$\pi/4$ | #$\sqrt{2}/2$ | #$\sqrt{2}/2$ | #$1$ | #
$60^o$ | #$\pi/3$ | #$\sqrt{3}/2$ | #$1/2$ | #$\sqrt{3}$ | #
$90^o$ | #$\pi/2$ | #$1$ | #$0$ | #$\infty$ | #