Chapter 7: Q. 3 (page 505)

Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (\sin \frac{11 π}{5})$

Short Answer

Expert verified

The exact value of the given expression is $\frac{π}{5}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$\sin^{- 1} (\sin \frac{11 π}{5})$

The composite function follows the form $f^{- 1} (f (x))$ , where $- \frac{π}{2} \leq x \leq \frac{π}{2}$ .

The value $\frac{11 π}{5}$ does not lie in the interval $[- \frac{π}{2}, \frac{π}{2}]$ .

Step 2. Determine where the quadrant lies.

The angle $\frac{11 π}{5}$ lies in the fourth quadrant. Therefore, the angle of $\frac{11 π}{5}$ is given by,

role="math" localid="1646502703272" $= \frac{11 π}{5} - 2 π = \frac{π}{5}$

The angle $\frac{π}{5}$ is in the interval $[- \frac{π}{2}, - \frac{π}{2}]$ and $\sin \frac{11 π}{5} = \sin (\frac{π}{5})$ .

Hence, $\sin^{- 1} (\sin \frac{11 π}{5}) = \frac{π}{5}$

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Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (\sin \frac{11 π}{5})$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine where the quadrant lies.

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Find the exact value of the expression. Express angles in radians.sin-1sin11π5

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine where the quadrant lies.

One App. One Place for Learning.

Most popular questions from this chapter

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Find the exact value of the expression. Express angles in radians.
$\sin^{- 1} (\sin \frac{11 π}{5})$