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`

Explanation:

Since, the graph of an inverse trigonometric function will pass through the point
`(1,(\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,(\pi)/(2))` is not satisfying function
`y=cos^(-1) x`,

⇒ The graph of
`y=cos^(-1) x` is not passing through the point
`(1,(\pi)/(2))`

For the function
`y=cot^(-1)x`

If x = 1

`y=cot^(-1)1=(\pi)/(4)`

Thus,
`(1,(\pi)/(2))` is not satisfying function
`y=cot^(-1)x`,

⇒ The graph of
`y=cot^(-1)x` is not passing through the point
`(1,(\pi)/(2))`

For the function
`y=sin^(-1) x`

If x = 1

`y=sin^(-1)1=(\pi)/(2)`

Thus,
`(1,(\pi)/(2))` is satisfying function
`y=sin^(-1) x`,

⇒ The graph of
`y=sin^(-1) x` is passing through the point
`(1,(\pi)/(2))`.

For the function
`y=tan^(-1)x`

If x = 1

`y=tan^(-1)1=(\pi)/(4)`

Thus,
`(1,(\pi)/(2))` is not satisfying function
`y=cos^(-1) x`,

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

Hence, Option C is correct.