HP persamaan sin(3x-15)°=¹/²√2 untuk 0°<x<180° adalah?

0° < x° < 180°
0° < 3x° < 540°
-15° < (3x - 15)° < 525°

sin(3x - 15°) = 1/²√2
(3x - 15)° = 45°, (180 - 45)°, (360 + 45)°, (540 - 45)°
3x - 15 = 45, 135, 405, 495
x - 5 = 15, 45, 135, 165
x = 20, 50, 140, 170

Sin(3x - 15) = sqrt(2) / 2
3x - 15 = Sin^-1(sqrt(2)/2)
3x - 15 = 45
3x 45 + 15 = 60
3x = 60
x = 20

sin(a) = √2/2 means
a = 45° + k*360° or a = 135° + k*360°
Where k = 0, ±1, ±2, ±3...
The values 45° and 135° come from asin(√2/2) and 180-asin(√2/2)

So let's go through the possibilities.
For k = 0:
3x - 15° = 45°
x = (45 + 15)° / 3 = 20° <<<<<<<<<<<<<<<<<<<
Also
3x - 15° = 135°
x = (135 + 15)° / 3 = 50° <<<<<<<<<<<<<<<<<<<

k = 1:
3x - 15° = 45° + 1*360° = 405°
x = (405 + 15)° / 3 = 140° <<<<<<<<<<<<<<<<<<<<<
3x - 15° = 135° + 1*360° = 495°
x = (495 + 15)° / 3 = 170° <<<<<<<<<<<<<<<<<<<<

k = 2:
3x - 15° = 45 + 2*360°
x = 260° (this doesn't work as it is > 180°, and neither will 135 + 2*360 or any of the higher k's).

So far that's 4 solutions. Check if any of the k = -1, -2, -3... work.