A graphing calculator shows four (4) zeros of f(x) = sin(2x -9°) -cos(x +30°) in the range 0° ≤ x ≤ 360°
Solutions are x ∈ {23°, 129°, 143°, 263°).
_____ You can make use of a couple of trig identities to rearrange this equation. cos(x) = sin(x+90°) sin(a) -sin(b) = 2*cos((a+b)/2)*sin((a-b)/2) So sin(2x -9°) -sin(x +120°) = 2*cos((3x +111°)/2)*sin((x -129°)/2) = 0 The cosine factor will be zero for (3x +111°)/2 = n*180° +90° 3x -69° = n*360° x = 23° +n*120° . . . . . . for any integer n The sine factor will be zero for (x -129°)/2 = n*180° x = 129° +n*360° . . . . . for any integer n
Combined, these solutions give the ones listed above in the range 0..360°.