# ACT Math Skill Review: Trigonometry

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

**SOHCAHTOA**:

SOH = **S**ine is **O**pposite over **H**ypotenuse.

CAH = **C**osine is **A**djacent over **H**ypotenuse.

TOA = **T**angent is **O**pposite over **A**djacent.

#### 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,*

**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

- Time Management
- Number Properties
- Fractions
- Arithmetic
- Order of Operations
- Algebraic Manipulation
- Word Problems
- Solving Equations
- Inequalities
- Linear Equations
- Miscellaneous Algebra
- Functions
- Ratios, Proportions and Variations
- Lines & Angles
- Triangles
- Quadrilaterals
- Circles
- Graphs and Coordinate Geometry
- Probability and Statistics
- Trigonometry

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