Answer:
Given the expression: [tex]\sin^{-1}(\cos(\frac{\pi}{2}))[/tex]
Let the value of the given expression in radians be [tex]\theta[/tex]
then;
[tex]\sin^{-1}(\cos(\frac{\pi}{2})) =\theta[/tex]
[tex]\cos \frac{\pi}{2} = \sin \theta[/tex] ......[1]
We know the value of [tex]\cos \frac{\pi}{2} = 0[/tex]
Substitute the given value in [1] we have;
[tex]\sin \theta = 0[/tex]
Since, the value of [tex]\sin \theta[/tex] is 0, therefore, the value of [tex]\theta[/tex] is in the form of:
[tex]\theta = n\pi[/tex] ; where n is the integer.
At n =0, 1 and 2, {Since, n is the integer}
Value of [tex]\theta =0, \pi[/tex] and [tex]2\pi[/tex]
therefore, the answer in radians either [tex] 0 , \pi[/tex] or [tex]2\pi[/tex]
