the graph of which function passes through the point $left(0,\frac{pi}{2}\right)$?\n$y = cos^{-1}(x)$\n$y =…

Explanation:

Step1: Substitute x = 0 into each function

We check the value of each inverse - trigonometric function when (x = 0).

Step2: Evaluate (y=\cos^{-1}(x)) at (x = 0)

Let (x = 0), then (y=\cos^{-1}(0)=\frac{\pi}{2}).

Step3: Evaluate (y = \csc^{-1}(x)) at (x = 0)

The function (y=\csc^{-1}(x)=\sin^{-1}(\frac{1}{x})), and (\frac{1}{0}) is undefined, so (y=\csc^{-1}(0)) is undefined.

Step4: Evaluate (y=\sec^{-1}(x)) at (x = 0)

The function (y = \sec^{-1}(x)=\cos^{-1}(\frac{1}{x})), and (\frac{1}{0}) is undefined, so (y=\sec^{-1}(0)) is undefined.

Step5: Evaluate (y=\sin^{-1}(x)) at (x = 0)

Let (x = 0), then (y=\sin^{-1}(0)=0).

Answer:

(y=\cos^{-1}(x))