Question

Use the unit circle to find the inverse function value in degrees.see image

Answer 1

Answer:

60°

Explanation:

We want to use the unit circle to find the inverse function value in degree:

$\tan^{-1}\sqrt{3}$

This means that we want to find an angle whose tangent is √3.

Consider the unit circle below:

We know that:

$\tan\theta=\frac{Opposite}{Adjacent}=\frac{y}{x}$

From the unit circle, at angle 60 degrees:

$\begin{gathered} (x,y)=(\frac{1}{2},\frac{\sqrt{3}}{2}) \\ \implies\frac{y}{x}=\frac{\sqrt{3}}{2}\div\frac{1}{2}=\frac{\sqrt{3}}{2}\times\frac{2}{1}=\sqrt{3} \end{gathered}$

Therefore:

$\tan60\degree=\sqrt{3}$

Thus, the inverse function value is 60 degrees.

Option 3 is correct.