4.3 Identities

Identities are equations that are always true.

5 + 2(x-3) = 2x - 1

5 + 2x-6 = 2x - 1

5 - 6 = -1

-1 = -1

Reciprocal Identities

sin(theta) = 1/csc(theta) csc(theta) = 1/sin(theta)

cos(theta) = 1/sec(theta) sec(theta) = 1/cos(theta)

tan(theta) = 1/cot(theta) cot(theta) = 1/tan(theta)

Quotient Identities

tan(theta) = sin(theta)/cos(theta) cot(theta) = cos(theta)/sin(theta)

Even/Odd Identities

sin(-theta) = -sin(theta) csc(-theta) = -csc(theta)

cos(-theta) = cos(theta) sec(-theta) = sec(theta) - (only even functions)

tan(-theta) = -tan(theta) cot(-theta) = -cot(theta)

Pythagorean Identities

a^2 + b^2 = c^2

(c x sinA)^2 + (c x cosA)^2 = c^2

c^2(sinA)^2

C^2 x sin^2A + c^2 x cos^2A= C^2

sin^2A + cos^2A = 1

sin^2(theta) + cos^2(theta) = 1

tan^2(theta) + 1 = sec^2(theta)

cot^2(theta) + 1 = csc^2(theta)