User:Jim.belk/Draft:List of trigonometric identities

Notation

Angles

This article uses Greek letters such as alpha (α), beta (β), gamma (γ), and theta (θ) to represent angles. Several different units for angle measure are widely used, including degrees, radians, and grads:

1 full circle  =  360 degrees  =  2$\pi$ radians  =  400 grads.

The following table shows the conversions for some common angles:

Degrees	30°	45°	60°	90°	120°	180°	270°	360°
Radians	$\pi /6$	$\pi /4$	$\pi /3$	$\pi /2$	$2\pi /3$	$\pi$	$3\pi /2$	$2\pi$
Grads	33⅓ grad	50 grad	66⅔ grad	100 grad	133⅓ grad	200 grad	300 grad	400 grad

Unless otherwise specified, all angles in this article are assumed to be in radians, though angles ending in a degree symbol (°) are in degrees.

Trigonometric functions

The primary trigonometric functions are the sine and cosine of an angle. These are usually abbreviated sin(θ) and cos(θ), respectively, where θ is the angle. In addition, the parentheses around the angle are sometimes omitted, e.g. sin θ and cos θ.

The tangent (tan) of an angle is the ratio of the sine to the cosine:

$\tan \theta ={\frac {\sin \theta }{\cos \theta }}.$

Finally, the reciprocal functions secant (sec), cosecant (csc), and cotangent (cot) are the reciprocals of the cosine, sine, and tangent:

$\sec \theta ={\frac {1}{\cos \theta }},\quad \csc \theta ={\frac {1}{\sin \theta }},\quad \cot \theta ={\frac {1}{\tan \theta }}={\frac {\cos \theta }{\sin \theta }}.$

These definitions are sometimes referred to as ratio identities.

Inverse functions

Main article: Inverse trigonometric functions

The inverse trigonometric functions are partial inverse functions for the trigonometric functions. For example, the inverse function for the sine, known as the inverse sine (sin⁻¹) or arcsine (arcsin or asin), satisfies

$\sin(\arcsin x)=x\!$

and

$\arcsin(\sin \theta )=\theta \quad {\text{for }}-\pi /2\leq \theta \leq \pi /2.$

This article uses the following notation for inverse trigonometric functions:

Function	sin	cos	tan	sec	csc	cot
Inverse	arcsin	arccos	arctan	arcsec	arccsc	arccot