Question

The graph of an inverse trigonometric function passes through the point (1, pi/2). Which of the following could be the equation of the function?
A) y=cos^-1 x
B) y=cot^-1 x
C) y=sin^-1 x
D) y=tan^-1 x

Answer 1

Answer: C) $y=sin^-1 x$

Step-by-step explanation:

Since, the graph of an inverse trigonometric function will pass through the point $(1,\frac{\pi}{2})$,

If this point satisfies the function,

For the function $y=cos^{-1} x$

If x = 1

$y=cos^{-1}1=0$

Thus,  $(1,\frac{\pi}{2})$ is not satisfying function  $y=cos^{-1} x$,

⇒ The graph of   $y=cos^{-1} x$ is not passing through the point  $(1,\frac{\pi}{2})$

For the function $y=cot^{-1}x$

If x = 1

$y=cot^{-1}1=\frac{\pi}{4}$

Thus,  $(1,\frac{\pi}{2})$ is not satisfying function $y=cot^{-1}x$,

⇒ The graph of   $y=cot^{-1}x$ is not passing through the point  $(1,\frac{\pi}{2})$

For the function $y=sin^{-1} x$

If x = 1

$y=sin^{-1}1=\frac{\pi}{2}$

Thus,  $(1,\frac{\pi}{2})$ is satisfying function $y=sin^{-1} x$,

⇒ The graph of   $y=sin^{-1} x$ is passing through the point  $(1,\frac{\pi}{2})$.

For the function $y=tan^{-1}x$

If x = 1

$y=tan^{-1}1=\frac{\pi}{4}$

Thus,  $(1,\frac{\pi}{2})$ is not satisfying function  $y=cos^{-1} x$,

⇒ The graph of   $y=tan^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$.

Hence, Option C is correct.