<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Finding Exact Trigonometric Values Using Double Angle Identities

Sine, cosine, and tangent of angles other than multiples of 30, 45, and 60 degrees.

Atoms Practice
Estimated8 minsto complete
%
Progress
Practice Finding Exact Trigonometric Values Using Double Angle Identities
Practice
Progress
Estimated8 minsto complete
%
Practice Now
Turn In
Finding Exact Trig Values using Double and Half Angle Formulas

You want to find the exact value of . How could you find this value without using a calculator?

Double Angle and Half Angle Formulas

In this concept, we will learn how to find the exact values of the trig functions for angles that are half or double of other angles. Here we will introduce the Double-Angle and Half-Angle Formulas.

Double-Angle and Half-Angle Formulas

The signs of and depend on which quadrant lies in. For and any formula can be used to solve for the exact value.

Let's find the exact value of .

is half of and in the first quadrant.

Now, let's find the exact value of if and .

To use the sine double-angle formula, we also need to find , which would be because is in the quadrant.

Finally, let's find the exact value of for from the previous problem.

Use to solve for .

Examples

Example 1

Earlier, you were asked to find the value of  without a calculator. 

so we can use the formula for

If we simplify this expression, we get .

Example 2

Find the exact value of .

is in the quadrant.

Example 3

Given the function  and , find .

First, find . , so

Example 4

Given the function  and , find .

You can use either formula.

Review

Find the exact value of the following angles.

The and . Find:

The and . Find:

Answers for Review Problems

To see the Review answers, open this PDF file and look for section 14.15. 

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Explore More

Sign in to explore more, including practice questions and solutions for Finding Exact Trigonometric Values Using Double Angle Identities.
Please wait...
Please wait...