AP Pre-Calculus Trigonometric Functions and Polar Coordinates Unit 3

Periodic

Y-values repeat over equal-length intervals.

Period

Shortest interval for function to repeat.

Radian

Angle measure based on arc length.

sin, cos, tan

Basic trigonometric functions for angles.

Unit Circle

Circle with radius 1 centered at origin.

Coordinates on Circle

(x, y) represent points on a circle.

Trigonometric Graphs

Visual representations of sin, cos, tan functions.

Graph of y = sin(θ)

Starts at midline, oscillates between -1 and 1.

Graph of y = cos(θ)

Starts at maximum, oscillates between -1 and 1.

Amplitude

Distance from midline to extrema in graphs.

Phase Shift

Horizontal displacement of trigonometric function graph.

Midline

Average of maximum and minimum values.

Period of Tangent

π radians; asymptotes at x = kπ.

Frequency

Cycles completed per second; reciprocal of period.

Inverse Trigonometric Functions

Functions that reverse sine, cosine, tangent operations.

Solving Trig Equations

Set equal to zero and solve for angles.

Reciprocal Functions

Functions like csc, sec, cot related to sin, cos, tan.

Sum/Difference Formulas

Formulas for sin(a ± b) and cos(a ± b).

Polar Coordinates

Coordinates defined by radius and angle.

Rectangular to Polar

Convert (x, y) to (r, θ) using formulas.

Complex Plane

Graphical representation of complex numbers.

Polar Graphs

Graphs defined by polar equations.

Extrema of Polar Graphs

Points where radius changes direction.

Average Rate of Change

Slope calculated using two points.

Estimating Values

Graphing helps find key points in functions.