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Chapter 6: Q. 21 (page 437)

find the value of the remaining five trigonometric functions of

tan蠎=-125蟺/2<蠎<蟺

Short Answer

Expert verified

the value of the remaining five trigonometric functions of 蠎are:

cos蠎=-513sin蠎=1213cosec蠎=1312sec蠎=-135cot蠎=-512

Step by step solution

01

Step 1. Given information

tan蠎=-125蟺/2<蠎<蟺

02

Step 2. Solving for  secϑ & cosϑ

We know that ;

tan2蠎+1=sec2蠎

Using this equation:

sec蠎=1+tan2蠎sec蠎=1+(-125)2sec蠎=1+14425sec蠎=16925sec蠎=135

Since theta is in second quadrant so;

sec蠎=-135

03

Step 3. Solving forcosϑ , sinϑ , cotϑ ,cosecϑ

We know that :

cosec蠎=1sin蠎sec蠎=1cos蠎cot蠎=1tan蠎

Using this :

cos蠎-513sin蠎=cos蠎脳tan蠎sin蠎=1213cot蠎=-512cosec蠎=1312

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