Question

How do you find the reference angle for 315 degrees?

Answer 1

Hint: We start solving the problem by recalling the definition of reference angle as the closest angle made with the x-axis regardless of the position where it ends up. We find the quadrant in which the given angle lies and then recall the fact that the positive x-axis is represented with $ {{0}^{\circ }} $ or $ {{360}^{\circ }} $ . So, we subtract the given angle from $ {{360}^{\circ }} $ to get the required answer for the problem.

Complete step by step answer:
According to the problem, we are asked to find the reference angle for 315 degrees.
Let us recall the definition of a reference angle.
We know that the reference angle is defined as the closet angle made with the x-axis regardless of the position where it ends up.
Now, let us find the reference angle for 315 degrees.
We know that the angles in the fourth quadrant are in the interval \[270\le \theta \le 360\]. So, the given angle lies in the fourth quadrant.
We know that the positive x-axis is represented with $ {{0}^{\circ }} $ or $ {{360}^{\circ }} $ .
Let us subtract the given angle from $ {{360}^{\circ }} $ to find the reference angle or $ {{315}^{\circ }} $ .
So, the reference angle is $ {{360}^{\circ }}-{{315}^{\circ }}={{45}^{\circ }} $ .
 $ \therefore $ We have found the reference angle for 315 degrees as $ {{45}^{\circ }} $ .

Note:
Whenever we get this type of problem, we first find the quadrant that the given angle lies in. We then check whether the given angle is closer to the positive or negative x-axis and then subtract it from the reference angle of the x-axis to get the required answer. We should keep in mind that the reference angle is always positive while solving this problem. Similarly, we can expect problems to find the reference angle for \[{{675}^{\circ }}\].