6.1 Fundamental Identities

Notes

An identity is an equation that is true for every value of the variable where both sides are defined.

• Reciprocal: $\displaystyle \csc x = \frac{1}{\sin x}$, $\displaystyle \sec x = \frac{1}{\cos x}$, $\displaystyle \cot x = \frac{1}{\tan x}$.
• Quotient: $\displaystyle \tan x = \frac{\sin x}{\cos x}$ and $\displaystyle \cot x = \frac{\cos x}{\sin x}$.
• Pythagorean: $\sin^2 x + \cos^2 x = 1$, $1 + \tan^2 x = \sec^2 x$, $1 + \cot^2 x = \csc^2 x$.
• Rearranged: $\sin^2 x = 1 - \cos^2 x$ and $\cos^2 x = 1 - \sin^2 x$.