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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 the angle is in Q1 (i.e. 0 < x < 90), then the angle itself is the reference angle. In other words, y = x
- If the angle is in Q2 (where 90 < x < 180), then y = 180-x
- If the angle x is in Q3 (where 180 < x < 270), then y = x-180.
- If the angle x is in Q4 (where 270 < x < 360), then y = 360-x is the reference angle.
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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