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Chapter 7: Q. 3 (page 505)

Find the exact value of the expression. Express angles in radians.

sin-1sin11蟺5

Short Answer

Expert verified

The exact value of the given expression is 蟺5.

Step by step solution

01

Step 1. Given information.

Consider the given question,

sin-1sin11蟺5

The composite function follows the form f-1fx, where -蟺2鈮�x鈮�蟺2.

The value 11蟺5does not lie in the interval -蟺2,蟺2.

02

Step 2. Determine where the quadrant lies.

The angle 11蟺5lies in the fourth quadrant. Therefore, the angle of 11蟺5 is given by,

role="math" localid="1646502703272" =11蟺5-2蟺=蟺5

The angle 蟺5is in the interval -蟺2,-蟺2and sin11蟺5=sin蟺5.

Hence,sin-1sin11蟺5=蟺5

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