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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Fundamentals of Trigonometric Identities
Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.
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Chapter 5.5, Problem 59E
To determine

To find:The exact values of the sinu2 , cosu2 and tanu2 using half-angle formula when cotu=3 and π<u<3π2 .

Expert Solution & Answer
Check Mark

Answer to Problem 59E

The exact values of the sinu2 , cosu2 and tanu2 are 50+151010 , −50−151010 and −10−3 , respectively.

Explanation of Solution

Given information:

  cotu=3 and π<u<3π2

Calculation:

Let the given value is cotu=3 . The angle is u and it ranges from π to 3π2 .

The value of sinu is calculated as,

  sinu=−(132+1)=−110=−1010

The value of cosu is calculated as,

  cosu=−(332+1)=−310=−31010

Write the expression to calculate the value of sinu2 .

  sinu2=1−cosu2

Substitute −31010 for cosu in the above equation.

  sinu2=1−(−31010)2=10+31020=50+151010

Write the expression to calculate the value of cosu2 .

  cosu2=1+cosu2

Substitute −31010 for cosu in the above equation.

  cosu2=−1+(−31010)2=−10−31020=−50−151010

Similarly, write the expression to calculate the value of tanu2 .

  tanu2=1−cosu2sinu2

Substitute −31010 for cosu2 and −1010 for sinu2 in the above equation.

  tanu2=1−(−31010)(−1010)=−(10+31010)=−10−3

Therefore, the exact values of the sinu2 , cosu2 and tanu2 are 50+151010 , −50−151010 and −10−3 , respectively.

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Chapter 5.5, Problem 58E
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Chapter 5.5, Problem 60E

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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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY