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Chapter 6: Q. 57 (page 396)

Find the exact value of each of the remaining trigonometric functions of 胃.

迟补苍胃=-13,蝉颈苍胃>0

Short Answer

Expert verified

The values of trigonometric functions are,

蝉别肠胃=-103肠辞蝉胃=-31010蝉颈苍胃=1010肠蝉肠胃=10

Step by step solution

01

Step 1. Given Information

Given that the trigonometric function is 迟补苍胃=-13,蝉颈苍胃>0.To find the exact values of trigonometric function using equation substitution.

02

Step 2. Solving a equation

It implies that 肠辞蝉胃<0,it appears in II quadrant which is 肠辞迟胃=-3.On using the equation to solve,

tan2胃+1=sec2胃蝉别肠胃=卤tan2胃+1

On substituting the equation,

蝉别肠胃=-1+(-13)2=-1+19蝉别肠胃=-103

03

Step 3. Solving the trigonometric function

On solving the rest of trigonometric function,

肠辞蝉胃=1sec胃=1-103肠辞蝉胃=-31010

On solving the equation of 蝉颈苍胃=卤1-cos2胃

It appears in II quadrant with 蝉颈苍胃>0.

蝉颈苍胃=1-cos2胃=1-(-31010)2蝉颈苍胃=1010肠蝉肠胃=1蝉颈苍胃=11010肠蝉肠胃=10

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