Question

Find the value of Sin^-1(tan π/4).

Answer 1

Answer:

D

Step-by-step explanation:

1. Remind that

$\tan \left(\dfrac{\pi }{4}\right)=1.$

Here you can use trigonometric table to find the value of $\tan\left(\dfrac{\pi}{4}\right)$, or you can remind that $\dfrac{\pi}{4}=45^{\circ}$ 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

$\sin^{-1}\left(\tan\left(\dfrac{\pi}{4}\right)\right)=\sin^{-1}1=\dfrac{\pi}{2},$

because

$\sin\dfrac{\pi}{2}=1.$