Evaluate each of the following: sin^-1(sin 13π/7)

Question

Evaluate each of the following:

\(sin^{-1}(sin\frac{13\pi}7)\)

Answer 1

We can write \((sin\frac{13\pi}7)\) as \(sin(2\pi-\frac\pi{7})\)

As we know sin(2π –θ) = sin(–θ )

So, \(sin(2\pi-\frac\pi{7})\) can be written as \(sin(\frac\pi{7})\)

∴ The equation becomes sin^–1\((sin\frac{\pi}7)\)

As sin^-1(sin x) = x

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

∴ we can write \(sin^{-1}(sin\frac{\pi}7)=\frac{\pi}7\)