Question

Which is equivalent sin^-1 (cos(pi/2))?Give your answer in radians

Answer 1

Answer:

Given the expression: $\sin^{-1}(\cos(\frac{\pi}{2}))$

Let the value of the given expression in radians be $\theta$

then;

$\sin^{-1}(\cos(\frac{\pi}{2})) =\theta$

$\cos \frac{\pi}{2} = \sin \theta$              ......[1]

We know the value of $\cos \frac{\pi}{2} = 0$

Substitute the given value in [1] we have;

$\sin \theta = 0$

Since, the value of $\sin \theta$ is 0, therefore, the value of $\theta$ is in the form of:

$\theta = n\pi$ ; where n is the integer.

At n =0, 1 and 2, {Since, n is the integer}

Value of  $\theta =0, \pi$ and $2\pi$

therefore, the answer in radians either   $0 , \pi$ or $2\pi$

Answer 2

Answer:

[A]  0

Step-by-step explanation:

Use the following identity:  cos(x) = sin( $\frac{\pi }{2}$ - x)

arcsin(cos($\frac{\pi }{2}$)) = arcsin(sin($\frac{\pi }{2}$ - $\frac{\pi }{2}$))

= arcsin(sin($\frac{\pi }{2} - \frac{\pi }{2}$))

Simplify:

arcsin(sin(0)) = 0

Hope this helps!