Find all the angles between 0 and 360 degree inclusive which satisfy the equation. (i) 3(sin x - cos x)=2 cos x, (ii) sin ( 2y -60 degree)=-1/2

Answer 1

If problem is find x where sin(2x) =b and b not equal to 1 or -1

then expect four answers in any one cycle

The answer above ignores 2x-60=-30,,,,from 2x-60=180-210+k*360,,,,k=0

x=15

check sin(2*15-60)=-.5

Answer 2

3(sinx - cosx) = 2cosx

3sinx -3cosx = 2cosx

3sinx = 5cosx

sinx/cosx = 5/3

tanx = 5/3

x = about 59.04 or 239.04 degrees

sin(2y-60)=-1/2

2y-60 = 210, 330, 570,

2y = 270, 390, 630,

y = 135, 195, 315,