Chapter 9: Q. 9 (page 632)

Find the exact value of $\sin^{- 1} (- \frac{1}{2})$ .

Short Answer

Expert verified

The value of $\sin^{- 1} (- \frac{1}{2})$ is $\frac{- π}{6}$ .

Step by step solution

Step 1. Given data

The given expression is

$\sin^{- 1} (- \frac{1}{2})$

Step 2. Expression value

Consider $\sin^{- 1} (- \frac{1}{2}) = θ$

then role="math" localid="1646857520718" $- \frac{1}{2} = \sin θ$

In interval role="math" $\frac{- π}{2} \leq θ \leq \frac{π}{2}$

role="math" localid="1646857602950" $\sin θ = - \frac{1}{2} \sin θ = \sin (\frac{- π}{6}) θ = \frac{- π}{6}$

Sorole="math" localid="1646857643826" $\sin^{- 1} (- \frac{1}{2}) = \frac{- π}{6}$

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Find the exact value of $\sin^{- 1} (- \frac{1}{2})$ .

Short Answer

Step by step solution

Step 1. Given data

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Find the exact value of $\sin^{- 1} (- \frac{1}{2})$ .