Find all the angles between 0 and 360 degree which satisfy the equations. (i) cos(2x+20 degree)= -0.5

Answer 1

cos(2x+20) = -.5

the angle is in quadrant II or III

reference angle is 60 degrees

2x+20= 180-60 or 180+60 or (180-60)+360 or (180+60)+360

2x+20 + 120, 240, 480 or 600

2x = 100, 220, or 460 or 580

x = 50, 110 or 230 or 290

Answer 2

cos(210 degrees)=-.866, not -.5

anyhow,

have

1. 2x+20=120+k*360,,,,cos(120)=-.5

and

2. 2x+20=-120+k*360

from equation 1., x=50+k*180

from equation 2. x=-70+k*180

x=50,230,110,290

check cos(600)=cos(2*290+20)