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Chapter 6: Q. 21 (page 435)

In Problems 16鈥�23, find the exact value of each of the remaining trigonometric functions.

tan胃=13,180掳<胃<270掳

Short Answer

Expert verified

The exact values of the remaining trigonometric functions of tan胃=13,180掳<胃<270掳are,

sin胃=-1010cos胃=-31010csc胃=-10sec胃=-103cot胃=3

Step by step solution

01

Step 1 Given expression is,

tan胃=13and 180掳<胃<270掳.

So,胃lies in the third quadrant and where tan胃is positive.

Let 伪be the reference angle for 胃then,tan胃=ba=tan伪.

So,tan伪=13=oppositeadjacent.

Use the values b=1,a=3to construct a triangle.

From the figure, we obtainr=10.

02

Step 2 Now calculate the remaining trigonometric functions.

The exact values of the remaining trigonometric functions of the reference angle 伪are,

sin伪=br=110cos伪=ar=310csc伪=rb=101=10sec伪=103cot伪=31=3

03

Step 3 The exact values of the trigonometric functions of the reference angle θ are,  

sin胃=-1010cos胃=-31010csc胃=-10sec胃=-103cot胃=3

These are the exact values of the remaining trigonometric functions.

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