Answer:
- sin(x) = ±(√2)/2
- r.a. = 45°
- x = 45° +k·360°
- x = 135° +k·360°
- x = 225° +k·360°
- x = 315° +k·360°
- x ∈ {135°, 225°, 315°, 405°}
Step-by-step explanation:
Start by solving for sin(x).
4sin(x)² = 2
sin(x)² = 1/2 . . . . divide by 4
sin(x) = ±√(1/2) = ±(√2)/2
Use your knowledge of the sine function to recognize that the reference angle is 45°, and that the angles x will be ...
x = ±45° or 180°±45° with multiples of 360° added
The solutions in the desired range are ...
x ∈ {135°, 225°, 315°, 405°}
