Problem
Give the degree measure of $\theta$ if it exists. Do not use a calculator. \[ \theta=\arctan \left(\frac{\sqrt{3}}{3}\right) \] Select the correct choice below and fill in any answer boxes in your choice. A. $\theta=$ (Type your answer in degrees.) B. $\arctan \left(\frac{\sqrt{3}}{3}\right)$ dees not exist
Solution
Step 1 ：The arctan function is the inverse of the tangent function. It returns the angle whose tangent is the input. In this case, we need to find the angle whose tangent is \(\frac{\sqrt{3}}{3}\).
Step 2 ：We know that \(\tan(30^{\circ}) = \frac{\sqrt{3}}{3}\). Therefore, \(\theta = 30^{\circ}\).
Step 3 ：Final Answer: \(\theta = \boxed{30^{\circ}}\)
