Trigonometric Identities

Includes: Definition of Trig Functions, Trig Functions on the Unit Circle, Reciprocal Trig Identities, Quotient Identities, Pythagorean Identities, Double Angle Identities, Sum and Difference Identities

sin θ

opp/hyp

cos θ

adj/hyp

tan θ

opp/adj

csc θ

hyp/opp

sec θ

hyp/adj

cot θ

adj/opp

sin θ (on the unit circle)

y

cos θ (on the unit circle)

x

tan θ (on the unit circle)

y/x

csc θ (on the unit circle)

1/y

sec θ (on the unit circle)

1/x

cot θ (on the unit circle)

x/y

sin θ (reciprocal trig identities)

1/(csc θ)

cos θ (reciprocal trig identities)

1/(sec θ)

tan θ (reciprocal trig identities)

1/(cot θ)

csc θ (reciprocal trig identities)

1/(sin θ)

sec θ (reciprocal trig identities)

1/(cos θ)

cot θ (reciprocal trig identities)

1/(cot θ)

tan θ (quotient identities)

(sin θ)/(cos θ)

cot θ (quotient identities)

(cos θ)/(sin θ)

sin² θ + cos² θ

1

1 + cot² θ

csc² θ

tan² θ + 1

sec² θ

sin(2θ)

2(sinθ)(cosθ)

cos(2θ)

cos² θ - sin² θ

cos(2θ)

1 - 2sin² θ

cos(2θ)

2cos² θ - 1

sin(α ± β)

sin(α) cos(β) ± cos(α) sin(β)

cos(α ± β)

cos(α) cos(β) ∓ sin(α) sin(β)