Question

find a value of θ in the interval 0°,90° that satisfies the given statement.
sin θ = 0.75943439
θ ≈ □°
(simplify your answer. type an integer or a decimal. round to six decimal places if needed.)

Explanation:

Step1: Use inverse sine function

To find \(\theta\) when \(\sin\theta = 0.75943439\) and \(\theta\in[0^{\circ},90^{\circ}]\), we use the inverse sine function \(\theta=\sin^{-1}(0.75943439)\).

Step2: Calculate using calculator

Using a calculator (in degree mode), we find \(\sin^{-1}(0.75943439)\approx49.399328^{\circ}\) (the value may vary slightly depending on the calculator's precision, but this is the approximate value when calculated correctly).

Answer:

\(49.399328\)