Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

find the exact value of the expression
sin 285 $°$ sin 75 $°$

$\sin 285 ° \sin 75 ° = - 0.9330127019$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Rewriting the expression

sin(270 $°$ +x)= $-$ cos(x )

sin285 $°$ =sin(270 $°$ +15 $°$ ) = $- \cos (15 °)$

Given expression becomes

sin 285 $°$ sin 75 $°$ = $-$ cos15 $°$ sin75 $°$

Step 2. Calculations

cos(90 $°$ $-$ x)=sin(x)

so, sin75 $°$ =cos(90 $° -$ 75 $°$ )=cos15 $°$

So now the expression becomes

$-$ cos15 $°$ cos15 $°$ = $- \cos^{2} (15 °)$

We know that

cos(2x)= $2 \cos^{2} x - 1$

role="math" localid="1646416466227" $\cos^{2} x = \frac{1 + \cos 2 x}{2} - \cos^{2} 15 ° = \frac{1 + \cos 30 °}{2} = \frac{1 + \frac{\sqrt{3}}{2}}{2} = - 0.9330127019$

Therefore,role="math" localid="1646416523469" $\sin 285 ° \sin 75 ° = - 0.9330127019$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

find the exact value of the expression
sin 285 $°$ sin 75 $°$

Step by Step Solution

Step 1. Rewriting the expression

Step 2. Calculations

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

find the exact value of the expression sin 285°sin 75°

Step by Step Solution

Step 1. Rewriting the expression

Step 2. Calculations

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find the exact value of the expression
sin 285 $°$ sin 75 $°$