10.1 Verifying Trigonometric Identities

The Fundamental Identities

There are four groups of fundamental identities: reciprocal identities, quotient identities, Pythagorean identities, and even-odd identities. The fundamental identities are used to establish other relationships among trigonometric functions.

Reciprocal Identities

sin x = 1 / csc x cos x = 1 / sec x tan x = 1 / cot x csc x = 1 / sin x sec x = 1 / cos x cot x = 1 / tan x

Even-Odd Identities

sin(-x) = - sin x cos(-x) = cos x tan (-x) = - tan x csc (-x) = - csc x sec (-x) = sec x cot (-x) = - cot x

Pythagorean Identities

sin²x + cos²x = 1 1 + tan²x = sec²x 1 + cot²x = csc²x

Quotient Identities

tan x = sin x / cos x cot x = cos x / sin x