ap precalc unit 3 review

The Unit Circle

A circle with radius 1 where cosθ = x and sinθ = y

Sine Function

The y-coordinate of a point on the unit circle

Cosine Function

The x-coordinate of a point on the unit circle

Tangent Function

The ratio of sine to cosine representing the slope of the terminal ray

Amplitude

Half the distance between the maximum and minimum values

Period

The horizontal distance for one full cycle (2π/|b| for sine/cosine)

Phase Shift

The horizontal translation of the graph

Midline

The horizontal line y=d that the graph oscillates around

Pythagorean Identity

sin²θ + cos²θ = 1

Reciprocal Identities

cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ

Double-Angle Identities

sin(2θ) = 2sinθcosθ and cos(2θ) = cos²θ - sin²θ

Inverse Sine

The angle θ in [-π/2, π/2] such that sinθ = x

Inverse Cosine

The angle θ in [0, π] such that cosθ = x

Inverse Tangent

The angle θ in (-π/2, π/2) such that tanθ = x

Polar Coordinates

Points (r, θ) defined by distance from the origin and angle from the polar axis

Rectangular to Polar

r² = x² + y² and tanθ = y/x

Polar to Rectangular

x = rcosθ and y = rsinθ

Polar Rose

Graphs defined by r = asin(nθ) or r = acos(nθ)

Polar Rate of Change

The distance from the origin increases when r and f'(θ) have the same sign