AP Precalculus Unit 3 Formula/Equation Memorization Practice

Arc Length Formula

s = ?

r = ?

θ = ?

s=rθ

s = arc length

r = radians

θ = central angle in radians

Sine, Cosine, and Tangent

sin = ?

cos = ?

tan = ?

sin = a/c

cos = b/c

tan = a/b

Trig Identities

tanθ = ?

secθ = ?

cscθ = ?

cotθ = ?

tanθ = sinθ / cosθ

secθ = 1 / cosθ

cscθ = 1 / sinθ

cotθ = cosθ / sinθ

Trig Identities: Derivations

sin²θ + cos²θ = 1

tan²θ + 1 = secθ (divided by cosθ)

1 + cot²θ = csc²θ (divided by sin²θ)

Trig Identities: Addition/Subtraction

sin(A+B) / (A-B) = ?

cos(A+B) / (A-B) = ?

sin(A+B) = sinAcosB + sinBcosA

sin(A-B) = cosAsinB - cosBsinA

cos(A+B) = cosAcosB - sinAsinB

cos(A-B) = cosAcosB + sinAsinB

Trig Identities: Other

sin(-θ) = ?

cos(-θ) = ?

sin(2x) = ?

cos(2x) = ?

sin(-θ) = -sin(θ)

cos(-θ) = cos(θ)

sin(2x) = 2sin(x)cos(x)

cos(2x) = cos²(x) - sin²(x)

Graphing Trigonometric Functions

Standard Formula

A = ?

B = ?

C = ?

D = ?

Period = ?

Asin(B(x + C)) + D

A = Amplitude

B = 2π / Period

C = Phase Shift (translation)

D = Midline

Period = 2π / B