Question

Find the exact value expression. tan^-1 (0)

Answer 1

Zero. The negative one means arctan. Arctan times 0 is 0. 

Answer 2

Hence, the exact value of the expression is:

0

Explanation:

We are given a expression as:

tan^-1 (0).

We have to find the value of a angle such that it is obtained on taking inverse of tangent of 0.

Let us consider,

Θ=tan^-1(0)

on taking tangent function on both side of the equation we get:

tan(θ)=tan(tan^-1(0))

tan(θ)=0

tan(θ)=tan(0)

since,

`\tan\theta=(\sin\theta)/(\cos\theta)`

Hence,

`\tan(0)=(\sin 0)/(\cos 0)\\\\\tan 0=(0)/(1)\\\\\tan 0=0`

Hence we get:

Θ=0.

Hence, the exact value of the expression is:

0