Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 6 - Analytic Trigonometry - Section 6.4 Trigonometric Identities - 6.4 Assess Your Understanding - Page 497: 41


The left side of the equation is equivalent to $3+\cos^2{\theta}$ therefore the given equation is an identity. Refer to the solution below.

Work Step by Step

\begin{align} $\text{LHS } &= 3 \sin^2{\theta} + 4 \cos^2{\theta} \\[3mm] &= 3 \sin^2{\theta} + 3 \cos^2{\theta}+\cos^2{\theta} \\[3mm] &= 3(\sin^2{\theta}+\cos^2{\theta})+\cos^2{\theta} \\[3mm] &= 3(1)+\cos^2{\theta} \\[3mm] &= 3+\cos^2{\theta} \\[3mm] &= 3+\cos^2{\theta} \\[3mm] &= \text{ RHS} \end{align}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.