Evaluate each of the following: sin^-1(sin 17π/8)

Question

Evaluate each of the following:

\(sin^{-1}\{(sin\frac{17\pi}8)\}\)

Answer 1

As we know sin(–θ) is –sin(θ )

∴ We can write \((sin\frac{-17\pi}8)\) as \(-sin(\frac{17\pi}8)\)

Now \(-sin(\frac{17\pi}8)\) = \(-sin(2\pi+\frac{\pi}8)\)

As we know sin(2π +θ) = sin(θ )

So \(-sin(2\pi+\frac{\pi}8)\) can be written as \(-sin(\frac{\pi}8)\)

And \(-sin(\frac{\pi}8)\) = \(sin(\frac{-\pi}8)\)

As sin^–1(sin x) = x

Provided x ∈ \([\frac{-\pi}2,\frac{\pi}2] \)

∴ we can write \(sin^{-1}(sin \frac{-\pi}8)=\frac{-\pi}8\)