Find the exact value of the real number $y$ if it exists. Do not use a calculator.
\[
y=\arctan (-1)
\]
Select the correct choice and fill in any answer boxes in your choice below.
A. $y=\arctan (-1)=$
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
B. $\arctan (-1)$ does not exist.
Answer
Final Answer: \(\boxed{y=\arctan (-1)= -\frac{\pi}{4}}\)
Step 1 ：The arctan function is the inverse of the tangent function. It returns the angle whose tangent is the input. The range of the arctan function is from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\).
Step 2 ：The tangent of an angle is negative in the second and fourth quadrants. Since the range of the arctan function is from \(-\frac{\pi}{2}\) to \(\frac{\pi}{2}\), the angle returned by the arctan function must be in the fourth quadrant if the input is negative.
Step 3 ：The angle in the fourth quadrant whose tangent is 1 is \(-\frac{\pi}{4}\).
Step 4 ：Final Answer: \(\boxed{y=\arctan (-1)= -\frac{\pi}{4}}\)
