PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 5, Problem 92CR
To determine

To calculate: The exact values of sin2u , cos2u and tan2u using the double-angle formulas.

Expert Solution & Answer
Check Mark

Answer to Problem 92CR

The required exact values of sin2u , cos2u and tan2u are tan2u are 835 , 59 and 52 respectively.

Explanation of Solution

Given information:

The function: cosu=−25 , π<u<3π2

Formula used:

Trigonometric formula:

  sin2A=2sinAcosA

  cos2A=1−2sin2A

  tan2A=2tanA1−tan2A

Calculation:

The function is cosu=−25 , π<u<3π2 .

Since, u lies in the quadrant III;

So, the values of x and y are positive and negative respectively.

Thus, r=22+(−5)2=4+5=9=3

Write the sine ratio as:

  sinu=−23

Now,

  tanu=sinucosu=−23−25=23×52=53

To find the exact value of sin2u , use the formula sin2A=2sinAcosA .

  sin2u=2sinucosu=2(−23)(−25)=835

To find the exact value of cos2u , use the formula cos2A=1−2sin2A .

  cos2u=1−2sin2u=1−2(−23)2=1−49=59

To find exact the value of tan2u , use the formula tan2A=2tanA1−tan2A .

  tan2u=2(53)1−(53)2=25949=259×9942=52

Hence, the required exact values of sin2u , cos2u and tan2u are 835 , 59 and 52 respectively.

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Chapter 5, Problem 91CR
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Chapter 5, Problem 93CR

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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