Find all angles θ between 0° and 180° satisfying the given equation.

Question

Find all angles θ between 0° and 180° satisfying the given equation. Round your answer to one decimal place. (Enter your answers as a comma-separated list.)

sin(θ) = 5/6

θ = ???

Answer 1

if sin(θ) = 5/6, then θ = arcsin(5/6) = 56.4^o (via calculator).

Since sin(180 - θ) = sin(θ), then we also have 180 - θ = 56.4, or θ = 180 - 56.4 = 123.6^o

^{Answer: 56.4, 123.6}

There are no other solutions in the range of 0 < θ < 180