EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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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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Question

Chapter 5.5, Problem 44E

To determine

the quadrant in which $u2$ lies.

Expert Solution

Answer to Problem 44E

Quadrant II

Explanation of Solution

Given:

$cotu=3$ , $π<u<3π2$

Given that $π<u<3π2$

This implies that u lies in the Quadrant III.

So, $u2$ will lie in the Quadrant II

To determine

To find: the exact vales of $sin(u2)$ , $cos(u2)$ and $tan(u2)$ .

Expert Solution

Answer to Problem 44E

$cosu2=−10−31020sinu2=10+31020tanu2=−3−10$

Explanation of Solution

Given:

$cotu=3$ , $π<u<3π2$

Formulas Used:

$cos2x=1+cos2x2$

$sin2x=1−cos2x2$

$tanx=sinxcosx$

It is known that,

$cotθ=31adjopp=31$

So, a right triangle can be imagined for which the side adjacent to $θ$ is 3 units and opposite side to $u$ is 1 unit in length. Then the hypotenuse of that triangle is given by,

Then,

$hyp=opp2+adj2=32+12=9+1=10$

Now since u lies in quadrant III and value of cosine is negative there, so,

$cosu=adjhyp=−310=−31010$

Consider,

$cos2u2=1+cosu2=1+(−31010)2=10−31020$

Since $u2$ lies in quadrant III and value of cosine is negative there, so,

$cosu2=−10−31020$

And

$sin2u2=1−cosu2=1−(−31010)2=10+31020$

Since $u2$ lies in quadrant III and value of sine is positive there, so,

$sinu2=10+31020$

And,

$tanu2=sinu2cosu2=10+31020−10−31020=−10+31010−310=−10+31010−310×10+31010+310$

$=−(10+310)2102−(310)2=−(10+310)100−90=−(10+310)10=−3−10$

Chapter 5.5, Problem 43E

Chapter 5.5, Problem 45E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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

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the quadrant in which u 2 lies.

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the quadrant in which u2<m:math><m:mrow><m:mfrac><m:mi>u</m:mi><m:mn>2</m:mn></m:mfrac></m:mrow></m:math> lies.

Answer to Problem 44E

Explanation of Solution

Answer to Problem 44E

Explanation of Solution

Chapter 5 Solutions

the quadrant in which $u2$ lies.