AP Exam Prep Reference Sheet (Unit 3) Vocabulary

A set of flashcards covering key trigonometric and function vocabulary from Unit 3 of the AP Exam Prep Reference Sheet.

Periodic Functions

Functions that demonstrate a repeating pattern as input values increase.

Amplitude

Half the difference between the maximum and minimum values of a sinusoidal function.

Midline

A horizontal line halfway between the maximum and minimum values of a sinusoidal function.

Sine Function

Gives the vertical displacement from the x-axis.

Cosine Function

Gives the horizontal displacement from the y-axis.

Frequency

The reciprocal of the period of a function.

Phase Shift

A horizontal translation of a sinusoidal function.

Transformations

Changes applied to functions including vertical and horizontal shifts, dilations, and translations.

Cotangent

The reciprocal of the tangent function.

Cosecant

The reciprocal of the sine function.

Secant

The reciprocal of the cosine function.

Inverse Trigonometric Functions

Functions that reverse the effect of the original trigonometric functions.

Polar Coordinates

Coordinates based on a radius and angle measuring the position in a polar system.

Sinusoidal Regression

A method to model sinusoidal functions for a given data set.

Pythagorean Identities

Trigonometric identities based on the Pythagorean theorem.

Parameter

An individual variable in a function that defines a particular case of the function.

Rectangular to Polar

The conversion of coordinates from rectangular format to polar format.

Radial Symmetry

A characteristic of polar graphs where the graph looks the same when rotated by certain angles.

Pythagorean Identities

\sin^2(\theta) + \cos^2(\theta) = 1, 1 + \tan^2(\theta) = \sec^2(\theta), and 1 + \cot^2(\theta) = \csc^2(\theta).

Sum Identities for Sine and Cosine

\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) and \cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta).

Difference Identities for Sine and Cosine

\sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta) and \cos(\alpha - \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta).

Double Angle Identity for Sine

\sin(2\theta) = 2\sin(\theta)\cos(\theta).

Double Angle Identities for Cosine

\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta), \cos(2\theta) = 2\cos^2(\theta) - 1, and \cos(2\theta) = 1 - 2\sin^2(\theta)