Question 1172631: https://imgur.com/a/GwImNIP
HI!hope you can help me
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! number 4:
the angle is 11pi/12
to convert that to degree measure, multiply it by 180/pi.
you will get 11pi/12 * 180/pi = 11/12 * 180 = 165 degrees.
that is an angle in the second quadrant.
number 5:
the reference angle would be 180 - 165 = 15 degrees.
number 6:
to find the negative coterminal angle of it, subtract 360 from it to get 165 - 360 = -195 degrees.
number 7:
to find the positive coterminal angle, add 360 to it to get -85 + 360 = 275 degrees.
number 8:
275 degrees is in the 4th quadrant.
to find the reference angle, subtract it from 360 degrees to get 360 - 275 = 85 degrees.
number 9:
to find the radian measure of it, multiply it by pi/180 to get:
275 * pi/180 = 275/180 * pi = 55/36 * pi = 55pi/36.
number 10:
you are given that the reference angle is 25 degrees.
you don't really have enough information to figure out what the angle is.
it could be in the first, second, third, or fourth quadrant.
if in the first quadrant, the angle would be 25 degrees.
if in the second quadrant, the angle would be 180 - 25 = 155 degrees.
if in the third quadrant, the angle would be 180 + 25 = 205 degrees.
if in the fourth quadrant, the angle would be 360 - 25 = 335 degrees.
assume the angle is in the first quadrant and your answer will be 25 degrees, the same as the reference angle.
number 11:
to find the negative coterminal angle, subtract 360 from it to get -335 degrees.
number 12:
the equivalent angle in radians will be 25 * pi/180 = 25/180 * pi = 5/36 * pi = 5pi/36.
i reproduced your table below.
here's what it looks like.
in general, the rules are:
to convert from radians to degrees, multiply the angle by 180 / pi.
to convert from degrees to radians, multiply the angle by pi / 180.
to find the reference angle, you need to convert your angle to an equivalent angle between 0 and 360 degrees.
if the angle is a positive angle greater than 360 degrees, just keep subtracting 360 from it until it gets between 0 and 360 degrees.
if the angle is a negative angle, just keep adding 360 to it until it gets between 0 and 360 degrees.
once the angle is between 0 and 360 degrees, do the following to find the reference angle.
if the angle is in the first quadrant between 0 and 90 degrees, leave it as is.
if the angle is in the second quadrant between 90 and 180 degrees, subtract it from 180.
if the angle is in the third quadrant between 180 and 270 degrees, subtract 180 from it.
if the angle is in the fourth quadrant between 270 and 360 degrees, subtract it from 360.
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