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Chapter 6: Q. 20 (page 437)

find the value of the remaining five trigonometric functions of 蠎

role="math" localid="1646316653225" cos蠎=233蟺2<蠎<2蟺

Short Answer

Expert verified

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

sin蠎=-53tan蠎=-52cosec蠎=-35sec蠎=32cot蠎=-25

Step by step solution

01

Step 1. Given information

cos蠎=233蟺2<蠎<2蟺

02

Step 2. Solving for sinϑ

We know ;

sin2蠎+cos2蠎=1

Using this :

sin蠎=1-cos2蠎sin蠎=1-(23)2sin蠎=1-49sin蠎=59sin蠎=53

Since theta is in fourth quadrant so,

sin蠎=-53

03

Step 3. Solving for cosecϑ , secϑ , cotϑ

We know ;

cosec蠎=1sin蠎sec蠎=1cos蠎cot蠎=1tan蠎

Using the above identities :

cosec蠎=-35sec蠎=32cot蠎=-25

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Most popular questions from this chapter

True or FalseThe only even trigonometric function are the cosine and secant functions.

In Problems 1-3, convert each angle in degrees to radians. Express your answer as a multiple of 蟺.

2.-400掳

graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

y=2csc13x-1

Find the exact value of each expression. Do not use a calculator.

3csc蟺3+cot蟺4

Convert each angle in degrees to radians. Express your answer as a multiple of 蟺.

270掳
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