Question

Find the value of Sin^-1(tan π/4).

Answer 1

D

Explanation:

1. Remind that

`\tan \left((\pi )/(4)\right)=1.`

Here you can use trigonometric table to find the value of
`\tan\left((\pi)/(4)\right)`, or you can remind that
`(\pi)/(4)=45^(\circ)` and
`\tan45^(\circ)=1` because special right triangle 45°-45°-90° is isosceles (with congruent oppposite and adjacent legs) and the ratio between the opposite leg and adjacent leg is equal to 1.

2. Now

`\sin^(-1)\left(\tan\left((\pi)/(4)\right)\right)=\sin^(-1)1=(\pi)/(2),`

because

`\sin(\pi)/(2)=1.`