Pre-Calculus A, 5th Hour, Winter 2012: 4.3: Identities

Identities: an identity is an equation that is always true

The following identities can be substituted in, in order to prove that one side of an equation is equal to the other.

Reciprocal Identities:

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

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

$tan\theta = \frac{1}{cot\theta }$ , $cot\theta = \frac{1}{tan\theta }$

Quotient Identies:

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

$cot\theta = \frac{cos\theta }{sin\theta }$

Even/Odd Identities

$sin \left ( -\theta \right )= -sin\theta$ , $csc \left ( -\theta \right )= -csc\theta$

$cos \left ( -\theta \right )= cos\theta$ , $sec \left ( -\theta \right )= sec\theta$

$tan \left ( -\theta \right )= -tan\theta$ , $cot \left ( -\theta \right )= -cot\theta$

cosine and secant are the only identities that are even

Pythagorean Identities:

$sin^{2}\theta + cos^{2}\theta =1$

$1+cot^{2}\theta =csc^{2}\theta$

$tan^{2}\theta +1= sec^{2} \theta$

Pre-Calculus A, 5th Hour, Winter 2012