Question

Find all solutions to 2 sin(theta) = sqrt(2) on the interval 0 less than or equal to theta less than 2 pi


Give your answers as exact values, as a list separated by commas.

Answer 1

2 sinØ = √2
sinØ = √2/2
from the 45-45-90 right-angled triangle you should recognize Ø = 45°

but the sine is positive in the I and II quads
so Ø = 45° or 135°
in radians , Ø = π/4 or 3π/4

Answer 2

thanks:)