notes/education/math/MATH1060 (trig)/Identities.md

Trigonometric Identities

All of the following only apply when the denominator is not equal to zero.

 tan \theta = \frac{y}{x} 

Because the following are inverses of their counterparts, you only need to remember the equivalents for sin, cos, and tan, then just find the inverse by taking 1/v.

Base Identity	Inverse Identity	Alternate Identities	Alternate Inverse Identities
sin\theta = y	csc\theta = \frac{1}{y}		csc\theta = \frac{1}{sin\theta}
cos\theta = x	sec \theta = \frac{1}{x}
tan\theta = \frac{y}{x}	cot\theta = \frac{x}{y}	tan\theta = \frac{sin\theta}{cos\theta}	cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}}

 cot \theta = \frac{x}{y} 

 sec\theta = \frac{1}{cos\theta}

 csc\theta = \frac{1}{sin\theta}

Pythagorean Identities

The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.

 sin^2 \theta + cos^2 \theta = 1