Question

I have no idea how to even begin this question. Thank you!

Answer 1

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°}