Appendix/Ramblings/TrigFunctions

Analytic Expressions for Selected Trigonometric Functions

In what follows we generally will provide expressions that result from evaluating $\sin \theta$, with the understanding that $\cos \theta$ and $\tan \theta$ then also can be evaluated straightforwardly via the familiar relations,

$\cos \theta$

$=$

$\pm (1-{\sin }^2\theta {)}^{1/2},$

and,

$\tan \theta$

$=$

$\frac{\sin \theta }{\pm (1-{\sin }^2\theta {)}^{1/2}}.$

Widely Used Evaluations

$0\le$ Angle $(\theta )\le \frac{\pi }{2}$		$\sin \theta$
Radians	Degrees
$0$	$0^{\circ }$	$0$
$\frac{\pi }{6}$	$30^{\circ }$	$\frac{1}{2}$
$\frac{\pi }{4}$	$45^{\circ }$	$\frac{\sqrt{2}}{2}$
$\frac{\pi }{3}$	$60^{\circ }$	$\frac{\sqrt{3}}{2}$
$\frac{\pi }{2}$	$90^{\circ }$	$1$

Integer-Degree Angles

A PDF-formatted document generated by James T. Parent lists exact values for the sine of all integer-degree angles between zero and ninety degrees, inclusive. An explanation of how the expressions in this document were derived, can be found on the SquareCirclez IntMath blog.