For each of these angles, determine the quadrant in which it terminates, its reference angle, and one positive and one negative coterminal angle

Question

A. 1120° 

B. (5π)/3

C. (-17π)/6

D. -480° 

Answer 1

1120/360 = 3 with remainder 40

40 is the reference angle

360-40= 320 degrees and -40 are the terminal angles in quadrant IV equivalent to 1120 degrees

5pi/3 has reference angle 5pi/3 - 3pi/3 = 2pi/3 = 120 degrees

reference angle is 60 degrees. 120-90= 60 or pi/3

terminal angles are 180-60 = 120 and 120-360 = -240

or 2pi/3 quadrant III and 2pi/3-6pi/3 =-4pi/3 radians quadrant III

-17pi/6 =-18pi/6 +pi/6 = -3pi +pi/6 is equivalent to -pi+pi/6 = -5pi/6 = -150 degrees quadrant III

equivalent to -150+360 = 210 degrees = 7pi/6 quadrant III

reference angle = 30 degrees = pi/6

-480 degrees + 360 = -120 = - 2pi/3 quadrant III

add 360 = 240 = 4pi/3 quadrant III

reference angle = 60 or pi/3