The principal value of sin -1((1/√2)) is

Question

The principal value of sin -1((1/√2)) is (A) (π/4) (B) (-π/4) (C) (3 π/4) (D) None of these

Tardigrade Admin · Accepted Answer

Let sin -1((1/√2))=y. Then, sin y=(1/√2). We know that, the range of the principal value branch of sin -1 is [(-π/2), (π/2)] and sin ((π/4))=(1/√2). Therefore, principal value of sin -1((1/√2)) is (π/4).

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

$\frac{π}{4}$

$\frac{- π}{4}$

$\frac{3 π}{4}$

None of these

Let $sin^{- 1} (\frac{1}{2}) = y$ . Then, $sin y = \frac{1}{2}$ .
We know that, the range of the principal value branch of $sin^{- 1}$ is $[\frac{- π}{2}, \frac{π}{2}]$ and $sin (\frac{π}{4}) = \frac{1}{2}$ . Therefore, principal value of $sin^{- 1} (\frac{1}{2})$ is $\frac{π}{4}$ .

Q. The principal value of sin−1(2​1​) is

4π​

4−π​

43π​