Concept preview

What you will be able to do

1. 01Use the reciprocal, quotient, and Pythagorean identities to simplify expressions
2. 02Prove identities by transforming one side into the other
3. 03Apply sum, difference, and double-angle formulas

Three families come straight from the definitions. Reciprocal: $$\csc\theta = \dfrac{1}{\sin\theta}$$, $\sec\theta = \dfrac{1}{\cos\theta}$, $\cot\theta = \dfrac{1}{\tan\theta}$. Quotient: $$\tan\theta = \dfrac{\sin\theta}{\cos\theta}$$ and $\cot\theta = \dfrac{\cos\theta}{\sin\theta}$. These let you rewrite any of the six trig functions in terms of sine and cosine — the single most useful move when simplifying or proving.