SOLUTION: Which of the following angles does not have a reference angle? A. 11pi/6 B. 5pi/6 C. -23pi/6 D. 7pi/6 E. 15pi/6

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Question 1197858: Which of the following angles does not have a reference angle?
A. 11pi/6
B. 5pi/6
C. -23pi/6
D. 7pi/6
E. 15pi/6

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Multiply each angle by the conversion factor (180/pi) to convert from radians to degrees.

For instance,
(11pi/6)*(180/pi) = 330
Showing that
11pi/6 radians = 330 degrees

The angle 330 degrees is not on the x axis nor y axis, so it does have an associated reference angle.

This angle is in quadrant IV, meaning
reference angle = 360-angle
reference angle = 360-330
reference angle = 30 degrees

Your task is to find which of the answer choices has an angle either on the x or y axis.
For instance, the angle 90 degrees does not have a reference angle since it's pointing directly north on the positive y axis. It's not in any of the four quadrants.

Let
x = input angle, something between 0 and 360
y = reference angle, some result between 0 and 90
Reference angle rules


If multiplying the radian measure by (180/pi) yields something outside the interval 0 < x < 360, then you'll need to add or subtract multiples of 360 so that you find a coterminal angle.

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