EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 5, Problem 63RE

To determine

To find: the exact value of $sin2u,cos2u$ and $tan2u$ , using the double angle formulas.

Expert Solution & Answer

Answer to Problem 63RE

$sin2u=2425cos(2u)=−725tan(2u)=−247$ .

Explanation of Solution

Given information:

Given trigonometric ratio

$sinu=45, 0<u<π2$ .

Calculation:

Consider the equation

$sinu=45, 0<u<π2$

Find $sin2u$ using double angle formula. The sine of an angle is equal to opposite side over the hypotenuse. Since;

$sinu=45$

Apply Pythagorean Theorem to find length of adjacent side;

$52−42=±9=±3$

Take only $3$ because $0<u<π2$ , draw the triangle;

EBK PRECALCULUS W/LIMITS, Chapter 5, Problem 63RE

Therefore;

$cosu=adjacentHypotenuse=35$

And,

$tanu=Oppositeadjacent=43$

Apply double angle formula $sin2u=2sinucosu$ . Substitute $sinu=45$ and $cosu=35$ ;

$sin2u=2(35)(45)=2425$

Therefore $sin2u=2425$

Apply double angle formula $cos2u=cos2u−sin2u$ . Substitute $sinu=45$ and $cosu=35$ ;

$cos2u=(35)2−(45)2=925−1625=−725$

Therefore $cos(2u)=−725$

Find $tan(2u)$ using double angle formula; apply double angle formula for tangent

$tan2u=2tanu1−tan2u$

Substitute; $tanu=43$

$tan2u=2(43)1−(43)2=(83−79)=−83(97)=−247$

Therefore;

$tan(2u)=−247$ .

Chapter 5, Problem 62RE

Chapter 5, Problem 64RE

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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the exact value of sin 2 u , cos 2 u and tan 2 u , using the double angle formulas.

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To find: the exact value of sin2u,cos2u<m:math><m:mrow><m:mi>sin</m:mi><m:mn>2</m:mn><m:mi>u</m:mi><m:mo>,</m:mo><m:mi>cos</m:mi><m:mn>2</m:mn><m:mi>u</m:mi></m:mrow></m:math> and tan2u<m:math><m:mrow><m:mi>tan</m:mi><m:mn>2</m:mn><m:mi>u</m:mi></m:mrow></m:math> , using the double angle formulas.

Answer to Problem 63RE

Explanation of Solution

Chapter 5 Solutions

To find: the exact value of $sin2u,cos2u$ and $tan2u$ , using the double angle formulas.