Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 1

Expert-verified

Precalculus Enhanced with Graphing Utilities

Found in: Page 500

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Find the exact value of the expression:
$\sin 195 ° \cdot \cos 75 °$

The exact value is $\frac{1}{2} [\frac{\sqrt{3}}{2} - 1]$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Consider the given question,

$\sin 195 ° \cdot \cos 75 °$

We know localid="1646458669499" role="math" $\sin a \cdot \sin b = \frac{1}{2} [\sin (a + b) + \sin (a - b)]$ .

Using the formula, we get,

$\sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\sin (195 ° + 75 °) + \sin (195 ° - 75 °)]$

Step 2. Simplify the equation.

Continuing the above equation,

$\sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\sin (270 °) + \sin (120 °)] \sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [- 1 + \frac{\sqrt{3}}{2}] \sin 195 ° \cdot \cos 75 ° = \frac{1}{2} [\frac{\sqrt{3}}{2} - 1]$

Most popular questions for Math Textbooks

If $z = \tan \frac{α}{2}$ , show that $\sin α = \frac{2 z}{1 + z^{2}}$ .

Establish each identity.

$\frac{\sin θ + \cos θ}{\sin θ} - \frac{\cos θ - \sin θ}{\cos θ} = s e c θ c s c θ$

$\sin (α - β) = \sin α \cos β___\cos α \sin β$

Repeat Problem $107$ for $g (x) = \cos^{2} x$ .

In Problems 9–36, find the exact value of each expression.

$\sec (\tan^{- 1} \sqrt{3})$

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free