# Trigonometry Basics & Practice Questions in ACT® Math Section The ACT Math exam includes 60 multiple-choice questions to be answered in 60 minutes. The questions covered on the exam are meant to assess your skills with concepts necessary for entry-level college courses. During the ACT Math exam, you are allowed to use a calculator. Your calculator must be approved at the ACT testing site. If you are unsure whether your calculator is prohibited, review the calculator policy available through ACT.org.

The ACT Math exam categorizes their questions into seven categories: Integrating Essential Skills, Number & Quantity, Algebra, Functions, Geometry, Statistics & Probability, and Modeling.

About seven to none of the questions on the ACT Math exam fall under the category of Geometry. ACT.org describes the skills necessary for geometry questions: “Understand [the] composition of objects, and solve for missing values in triangles, circles, and other figures, including using trigonometric ratios and equations of conic sections.” To perform successfully with geometry questions, you need to have a strong understanding of ACT trigonometry basics.

This article will break down some basic formulas and concepts used to solve for missing values in triangles. Skills with these basics are important for ACT Math questions centered around more complex trigonometry.

Here are some examples of basic trigonometry questions:

1. Which of the following is equivalent to sin θ csc(–θ) wherever sin θ csc(–θ) is defined?
a. __
b. __
c. __
d. __

2. Which of the following is the sine of angle A in the right triangle below?
a. __
b. __
c. __
d. __

A number of questions will ask you to solve for missing values in triangles. Trigonometric formulas can help you with this task. Use this information as a baseline for the geometry questions.

### How to Find Sine

The formula for sin (θ) is b/c , where b represents the line opposite the angle, and c represents the hypotenuse.

To solve a problem that asks you to find sin, divide the opposite by the hypotenuse.
When graphing sin, use this formula: y=sin x
A graph for sine will look something like this:

### How to Find Cosine

The formula for cos(θ) is a/c , where a represents the line adjacent to the angle and c represents the hypotenuse.

To solve a problem that asks you to find cosine, divide the adjacent by the hypotenuse.
When graphing cosine, use this formula: y= cos x
A graph of cosine will look something like this:

### How To Find Tangent

The formula for tan (θ) is b/a , where b represents the line opposite from the angle and a represents the line adjacent to the angle.

When graphing for tan, use this formula: y= tan x
A graph for tangent will look something like this:

During the ACT Math exam, you may come across questions that ask you to find the sine of a triangle given its tangent and a range of the measure of the angle. Other questions will require you to select the proper equation for solving the sine, cosine, or tangent of a given triangle.

As you prepare for the exam, consider these ACT trigonometry basics. You can practice applying them to more complicated Math problems using UWorld’s ACT Prep Course. The prep course offers ACT trigonometry practice questions that are realistic to the style and level of difficulty that you will work with on the official ACT exam. You should also know that the prep course offers detailed answer explanations to deepen your understanding of more complicated concepts or help you learn from your mistakes.

The performance tracking tool offered in the prep course is a great resource for tracking your improvements as you prepare. It is also helpful in pinpointing the sections, subsections, and question types that you can work on to improve your score.

If you find that you struggle with geometry questions on the ACT Math exam, consider going back to the basics and solving ACT trigonometry practice questions. You can use this page as a reference. Try our prep course to streamline your study plan and improve your scores!

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