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Chapter 6: Q. 56 (page 395)

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

肠辞迟胃=43,肠辞蝉胃<0.

Short Answer

Expert verified

The exact values for trigonometric functions are,

蝉别肠胃=-54肠辞蝉胃=-45蝉颈苍胃=-35肠蝉肠胃=-53

Step by step solution

01

Step 1. Given Information

Given that the trigonometric function is 肠辞迟胃=43,肠辞蝉胃<0.To find the exact values of trigonometric functions using substitution.

02

Step 2. Solve a equation

It implies 蝉颈苍胃<0where lies in III quadrant. On using the equation of 蝉别肠胃=卤tan2胃+1.

蝉别肠胃=-1+342=-1+916蝉别肠胃=-54肠辞蝉胃=1蝉别肠胃肠辞蝉胃=-45

03

Step 3. Substitution

On using the equation for substitution,

蝉颈苍胃=卤1-cos2胃=-1-(-45)2=-1-1625蝉颈苍胃=-35肠蝉肠胃=1蝉颈苍胃=1-35肠蝉肠胃=-53

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