The principal value of sin -1( -(√3/2) ) is:

Question

The principal value of sin -1( -(√3/2) ) is: (A)  (4π /3)  (B)  (5π /3)  (C)  -(2π /3)  (D)  -(π /3)

Tardigrade Admin · Accepted Answer

The principal value of sin -1x is -(π /2) to (π /2). We have sin -1( -(√3/2) )=θ ⇒ sin θ =-(√3/2) =- sin (π /3) = sin ( -(π /3) ) ∴ Principal value is ( -(π /3) ).

Q. The principal value of $sin^{- 1} (- \frac{3}{2})$ is:

$\frac{4 π}{3}$

$\frac{5 π}{3}$

$- \frac{2 π}{3}$

$- \frac{π}{3}$

The principal value of $sin^{- 1} x$
is $- \frac{π}{2}$ to $\frac{π}{2} .$
We have $sin^{- 1} (- \frac{3}{2}) = θ$
$\Rightarrow$ $sin θ = - \frac{3}{2}$
$= - sin \frac{π}{3}$
$= sin (- \frac{π}{3})$
$∴$ Principal value is
$(- \frac{π}{3}) .$

Q. The principal value of sin−1(−23​​) is:

34π​

35π​

−32π​

−3π​