AP Pre-Calc Formulas

Use as flashcards. Write down the formulas on a piece of paper to ensure memorization.

Rate of Change

Arithmetic Sequence

a_n = d (n - 1) + c

Geometric Sequence

(a)(r^n-1)

Quadratic Function

f(x) = ax² + bx + c

Vertex Form

f(x) = a(x - h)² + k

Exponential Function

y = a * b^x

tan(x)

sin(x)/cos(x)

cot(x)

1/tan(x) = cos(x)/sin(x)

sec(x)

1/cos(x)

csc(x)

1/sin(x)

Pythagorean Identity (1)

sin²θ + cos²θ = 1

Pythagorean Identity (2)

1 + cot²θ = csc²θ

Pythagorean Identity (3)

tan²θ + 1 = sec²θ

sin(a + b)

sin(a)cos(b) + cos(a)sin(b)

cos(a + b)

cos(a)cos(b) − sin(a)sin(b)

sin(2θ)

2sin(θ)cos(θ)

cos(2θ)

cos²(θ) − sin²(θ)

cos(-θ)

cos(θ)

sin(-θ)

-sin(θ)

sin(a − b)

sin(a)cos(b) − cos(a)sin(b)

cos(a − b)

cos(a)cos(b) + sin(a)sin(b)

r [polar coordinates]

√(x² + y²)

θ [polar coordinate]

tan⁻¹(y/x)

x [Rectangular Coordinates]

r cos(θ)

y [Rectangular Coordinate]

r sin(θ)