What is the reference angle for 210 degrees?
To find the reference angle for an angle in standard position,
1. Draw the angle in standard position, rotated from the right
side of the x-axis, counter-clockwise if the angle is positive
and clockwise if the angle is negative.
2. Calculate the acute angle not in standard position between
the terminal side and the x-axis.
So, for your peoblem:
1. We draw the angle of 210° in standard position:
2. We draw the reference angle, which is the acute angle which is not
in standard position between the terminal side of the 210° angle and
the x-axis, shown by the red arc below.
The reference angle is the amount of rotation more than 180² the 210°
extends into the third quadrant. So the reference angle is calculated
by subtracting 180° from 210°. So the reference angle indicated by the
the red arc is 210° - 180° = 30°.
So that's the answer. The reference angle is always the acute angle
between the terminal side and the x-axis.
Edwin
