Q52 - Trigonometric equations and inequalities

The correct answer is A) 1.

Put θ = (x + 90°)/10. Then sin⁴θ = 1/16 means sin θ = ±1/2.

The important part is the range: as x goes from 0° to 360°, θ only goes from 9° to 45°. In that range sine is positive, and sin θ = 1/2 only at θ = 30°, which gives x = 210°.

So there is just one solution. If you forget that dividing by 10 shrinks the range, you'll count far too many.