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Q63.

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Precalculus Mathematics for Calculus
Found in: Page 418
Precalculus Mathematics for Calculus

Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

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Short Answer

Find the values of the trigonometric functions of t from the given information.

sint=−45, terminal point of t is in Quadrant IV

The values of the trigonometric functions are cost=35,tant=−43,csct=−54,sect=53, and cott=−34.

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1. State the Trigonometric identities.

The reciprocal identities are csct=1sint,sect=1cost,cott=1tant,tant=sintcost and cot=costsint.

The Pythagorean identities are:

1. sin2t+cos2t=1

2. tan2t+1=sec2t

3. cot2t+1=csc2t

Step 2. Formula used. 

Now use Pythagorean Identity sin2t+cos2t=1, substitute −45 for sint and simplify for cost.

sin2t+cos2t=1 −452+cos2t=11625+cos2t−1625=1−1625 cos2t=925 cost=±35

Now, t is given to be in quadrant IV, and quadrant IV, cost>0, therefore, cost=35.

Now substitute −45 for sint for 35and cost into reciprocal identity tant=sintcost and simplify for tant.

tant=sintcost =−4535 =−43

Step 3. Find other trigonometric functions.

Use the values of sint,cost and tant to find csct,sect and cott.

csct=1sint

=1−45=−54

sect=1cost

=135=53

cott=1tant

=1−43=−34

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