Answer:
x = 80°
Step-by-step explanation:
The relationship between sine and cosine can be written as ...
cos(x) = sin(90° +x)
So, we can rewrite the given equation as ...
sin(0.5x -30°) = sin(x +90°)
Taking the inverse sine function of both sides, we get two equations:
- 0.5x -30° = x +90°
- 0.5x -30° = 180° -(x +90°)
because the sine of an angle is also equal to the sine of its supplement.
Solving the first of these equations gives ...
-120° = 0.5x ⇒ x = -240° . . . . not in the desired domain
The second of these equations gives ...
1.5x = 120° ⇒ x = 80° . . . . . the solution we seek
The solution is x = 80°.
_____
Check
Filling in the value for x gives ...
sin(80°/2 -30°) = cos(80°) . . . . true
_____
A graphing calculator confirms this result.
