If 𝑠𝑖𝑛²𝜃 = 3/4 , find all possible values for 𝜃, where −180° < 𝜃 < 180°

Question

Don't really understand the question, any help would be greatly appreciated :)

Answer 1

sin^2 = 3/4, then sin = +/- sqrt(3)/2, which occurs at 60 degrees, 120 degrees, -120 degrees and -60 degrees.

Answer 2

Hi Cavan:

Here's the approach: sin²Θ = 3/4 => sinΘ = ±√3 / 2 (check this out on your standard 30-60-90 triangle

Now, the primary angle in Q1 with sin = √3 / 2 is Θ = π/3

Therefore, for the positive square root, the first 2 solutions are π/3 and π - π/3 = 2π/3

For the negative square root, we have π + π/3 = 4π/3 and 2π - π/3 = 5π/3

Solution set = {π/3; 2π/3; 4π/3; 5π/3}