Find all the angles between 0 and 360 degrees which satisfy the equation. (i) sin x+3 cos x=0 (ii) sin (2y+60degree)= -0.5

Answer 1

sin(2y+60) =-.5

2y +60 = 210, 330, 570, 690,

2y = 150, 270, 510, 630

y = 75, 135, 255, 315

sinx +3cosx = 0

sinx =-3cosx

sinx/cosx =-3

tanx = -3

x = tan^-1(-3) = reference angle of 71.6, but

x is in quadrant II or IV where tangents are negative

x = about 180-71.6 or 360-71.6

x = about 108.4 or 288.4 degrees