Question 1112429
first you find the equivalent positive angle between 0 and 360 degrees.


just subtract 360 from 960 until you get there.


960 - 360 = 600 - 360 = 240


the equivalent angle between 0 and 360 degrees is 240 degrees.


that angle is in the third quadrant.


the reference angle for an angle in the third quadrant is that angle minus 180 degrees.


240 - 180 = 60 degrees.


that's your reference angle.


you can use your calculator to confirm.


if the angle is the reference angle, then the sine and cosine and tangent of the angle will be the same as the sine and cosine and tangent of the reference angle except for the sign.


the sine in the third quadrant is negative.
the cosine in the third quadrant is negative.
the tangent in the third quadrant is positive.


using my calculator, i get:


sin(60) = + .8660254038
cos(60) = + .5
tan(60) = + 1.732050808


sin(240) = - .8660254038
cos(240) = - .5
tan(240) = + 1.732050808


the trig functions are the same except for the sign, therefore 60 degrees is the reference angle for 240 degrees.


to confirm that 240 degrees is equivalent to 960 degrees, i got the trig functions for 960 degrees, using my calculator.


sin(960) = - .8660254038
cos(960) = - .5
tan(960) = + 1.732050808


that's identical to the trig functions for 240 degrees, therefore 960 degrees and 240 degrees are equivalent.