AP Precalculus – Trigonometric and Polar Functions: Core Vocabulary

These flashcards review the essential vocabulary for understanding sine, cosine, tangent, and related sinusoidal concepts using the unit circle.

Unit Circle

A circle of radius 1 centered at the origin; used to define the sine, cosine, and tangent of any real-number angle.

Angle in Standard Position

An angle whose vertex is at the origin and whose initial side lies on the positive x-axis.

Radian Measure

An angle measure equal to the ratio of an arc’s length to the circle’s radius; 2π radians = 360°.

Coterminal Angles

Angles in standard position that share the same terminal side, differing by integer multiples of 360° (or 2π radians).

Sine Function (sin θ)

For an angle θ on the unit circle, sin θ equals the y-coordinate of the terminal point.

Cosine Function (cos θ)

For an angle θ on the unit circle, cos θ equals the x-coordinate of the terminal point.

Tangent Function (tan θ)

Defined as sin θ ⁄ cos θ; geometrically, the slope of the line from the origin to the terminal point.

Periodic Phenomenon

Any behavior that repeats at fixed intervals, such as wave motion, modeled by trigonometric functions.

Sinusoidal Function

A function expressible as A sin(Bx + C) + D or A cos(Bx + C) + D; graphs are smooth, repetitive waves.

Amplitude

Half the distance between a sinusoid’s maximum and minimum values; numerically |A| in the standard form.

Period (of a Sinusoid)

The horizontal length of one complete cycle; equal to 2π ⁄ |B| in A sin(Bx + C) or A cos(Bx + C).

Phase Shift

The horizontal translation of a sinusoidal graph, given by −C ⁄ B in the function A sin(Bx + C) or A cos(Bx + C).

Vertical Shift

The constant D that moves a sinusoidal graph up or down relative to the x-axis.

Tangent Function Graph

A curve with period π, vertical asymptotes where cos θ = 0, and roots where θ = kπ.