How do you solve

Question

sin x * cos x = 1/4

I don't know where to start.

Answer 1

An important identity is
sin (2x) = 2sinxcosx

so if
sinx cosx = 1/4
2sinx cosx = 1/2
sin (2x) = 1/2
2x = 30° or 2x = 150°
x = 15° or x = 75°

since the period of sin (2x) = 360°/2 or 180°,
other solutions are 15+180 or 195°
and 75+180 or 255°

in radians: π/12, 5π/12, 13π/12, and 17π/12

testing one of them:
sin 195° * cos 195° = .25 , looks good