 Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q32.

Expert-verified Found in: Page 488 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Evaluating an ExpressionEvaluate the expression without using a calculator${\left(sin{60}^{°}\right)}^{\mathbf{2}}\mathbf{+}{\left(cos{60}^{°}\right)}^{\mathbf{2}}$

The answer of the expression is 1.

See the step by step solution

## Step 1. Given information

A trigonometric expression is given as ${\left(\mathrm{sin}{60}^{°}\right)}^{2}+{\left(\mathrm{cos}{60}^{°}\right)}^{2}$.

## Step 2. Concept used

To simplify the problem, use trigonometric ratios. Replace the ratio values in the expression and do the calculation. For more simplification, utilize trigonometric identities.

## Step 3. Calculation

The given expression is ${\left(\mathrm{sin}{60}^{°}\right)}^{2}+{\left(\mathrm{cos}{60}^{°}\right)}^{2}$, substitute the values as-

$\begin{array}{l}\because \mathrm{sin}{60}^{°}=\frac{\sqrt{3}}{2}&\mathrm{cos}{60}^{°}=\frac{1}{2}\\ ={\left(\frac{\sqrt{3}}{2}\right)}^{2}+{\left(\frac{1}{2}\right)}^{2}\\ =\frac{3}{4}+\frac{1}{4}\\ =\frac{4}{4}\\ =1\end{array}$ ### Want to see more solutions like these? 