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.)
cos(θ)=\frac{5}{8}
θ =
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Explanation:

Step1: Use inverse - cosine function

$\theta=\cos^{-1}(\frac{5}{8})$

Step2: Calculate the value

Using a calculator, $\cos^{-1}(\frac{5}{8})\approx51.3^{\circ}$
Since the cosine function is positive in the first and fourth quadrants, and we want angles between $0^{\circ}$ and $180^{\circ}$, the only solution in this range is the angle in the first - quadrant.

Answer:

$51.3^{\circ}$