Question

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

sin() =
7
8

Answer 1

nothing to it, it's just the sin⁻¹(θ)

`sin(\theta )=\cfrac{7}{8}\implies \theta =sin^(-1)\left( \cfrac{7}{8} \right)\implies \theta \approx \begin{cases} 61.0^o\\ 119.0^o \end{cases}`

let's recall that the inverse sine function has a range from π/2 to -π/2, so whatever angle it's going to spit out will be on those quadrants, so to get the one on the II Quadrant in this case, the 119° one, we use the reference angle, as you can see in the picture below, always make sure your calculator is in the proper mode, either Radians if you need radians or Degree if you need degrees.