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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Chapter 5.1, Problem 10E
To determine

To calculate: The values of all six trigonometric functions.

Expert Solution & Answer
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Answer to Problem 10E

The required values of sinx , cosx , tanx , cotx and cscx are 215 , −25 , −212 , −221 and 521 respectively.

Explanation of Solution

Given information:

The function: tanϕ=−73 , cosϕ<0

Formula used:

Trigonometric identities:

  sinx=1cscx

  secx=1cosx

  tanx=sinxcosx

  cotx=1tanx

  cos2x+sin2x=1

Calculation:

The given function is tanϕ=−73 .

So, cotϕ=1tanϕ=1−73=−37

It is known that sec2ϕ=1+tan2ϕ .

Use the above formula to find secϕ .

  secϕ=1+tan2ϕ=1+(−73)2=1+499=583

So, cosϕ=1secϕ=1583=358

To find the value of sinϕ , use the formula cos2ϕ+sin2ϕ=1 .

  cos2ϕ+sin2ϕ=1sin2ϕ=1−cos2ϕsinϕ=1−(358)2=4958=758

So, cscϕ=1sinϕ=1758=587

Hence, the required values of sinϕ , cosϕ , cotϕ , secϕ and cscϕ are 758 , 358 , 587 , 583 and 587 respectively.

Previous
Chapter 5.1, Problem 9E
Next
Chapter 5.1, Problem 11E

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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