Precalculus Trigonometric Identities

Flashcards covering trigonometric identities, Pythagorean identities, sum and difference identities, and double angle identities.

Trigonometric Identity

An equation that is always true. These allow us to manipulate trigonometric expressions and rewrite these expressions in equivalent forms using various trig functions.

tan x

sin(x)/cos(x)

cot x

cos(x)/sin(x)

csc x

1/sin(x)

sec x

1/cos(x)

Pythagorean identity for trigonometric functions

For any angle, the square of the sine of the angle plus the square of the cosine of the angle always equals 1.

Pythagorean Identity

sin²θ + cos²θ = 1

Pythagorean Identity tan

1 + tan²θ = sec²θ

cot Pythagorean identity

1 + cot²θ = csc²θ

x =

cos(θ)

y =

sin(θ)

Sum Identity for Sine

sin(α + β) = sin α cos β + cos α sin β

Sum Identity for Cosine

cos(α + β) = cos α cos β - sin α sin β

Sum and Difference Identities for Sine

sin(α ± β) = sin α cos β ± cos α sin β

Sum and Difference Identities for Cosine

cos(α ± β) = cos α cos β ∓ sin α sin β

sin(2θ) =

2sin(θ)cos(θ)

cos(2θ) =

cos²(θ) - sin²(θ) = 1 - 2sin²(θ) = 2cos²(θ) - 1