ACT Math Skill Review: Trigonometry

Basic trigonometry is based on the relationships between the sides of a right triangle and a corresponding angle.

An easy way to remember the trigonometric functions is the acronym SOHCAHTOA:

SOH = Sine is Opposite over Hypotenuse.
CAH = Cosine is Adjacent over Hypotenuse.
TOA = Tangent is Opposite over Adjacent.

Other Important Trigonometric Functions and Relationships

Graphs of Trigonometric Functions

You will be expected to be able to identify the graph of a trigonometric function from a given equation or to find an equation from a given graph. The general equation for a given trigonometric function is represented by:

y = AsinBO,

where A is the amplitude of the graph (how tall the graph is) and B is the period of the graph (how long it takes to get through a complete cycle.,

Thus, an increase is A also increases the amplitude or height of the graph (a direct relationship). Increases in B result in a decrease in the period (an inverse relationship).

Below are the graphs of the simple functions y=sin x and y = cos x, respectively:

y = sin x



y = cos x

Examples

Answers and Explanations