Question

What is the method for determining the reference angle for the angle 220?

Answer 1

Hint: We must find the reference angle for the provided angle in this question. To do so, we must first understand what a reference angle is. The terminal side of a reference angle is in the second, third, or fourth quadrant. A reference angle is always less than 90 degrees, i.e., an acute angle.

Complete step by step answer:
A reference angle's beginning side is on the positive x-axis, while its terminal side is in the first quadrant. The absolute difference between any angle and the nearest multiple of 180 is the reference angle. The reference angle is the angle between the supplied angle and the x-axis, to use one example.
We know the reference angle 200 is the reflex angle and always resides in the third quadrant. Because 220 degrees is 20 degrees more than 180 degrees, it is a reflex angle in the third quadrant.
We will find the nearest multiple of 18o degree to 220 degree is 180 degrees.
So, the reference angle of 220 is
\[ \Rightarrow {220^ \circ } - {180^ \circ } = {40^ \circ }\]
Hence, the reference angle for the angle 220 is 40.

Note:To get the reference angle of a negative angle, first convert it to a positive angle by adding it to the full angle (360), and then determine the quadrant in which the angle is located. Because each quadrant is 90 degrees, if an angle is in the second quadrant, it is subtracted by 90 degrees. If the angle falls inside the third quadrant, we remove 180 degrees, and if it falls within the fourth quadrant, we subtract 270 degrees.