Find all the values of ø between 0⁰and 360⁰ satisfying the equation 5 sin ø= 4

March 16, 2026Mathematics

ScanSolve AI Answer

Answer

53.13^\circ, 126.87^\circ

6 steps

Start with the given equation.
$5 \sin \theta = 4$
Divide both sides by 5.
$\sin \theta = \frac{4}{5} = 0.8$
$\sin \theta = 0.8 > 0$ , so solutions are in the first and second quadrants between $0^\circ$ and $360^\circ$ .
Reference angle $\alpha = \sin^{-1}(0.8)$ .
$\alpha \approx 53.13^\circ$
First quadrant solution.
$\theta_1 = 53.13^\circ$
Second quadrant solution.
$\theta_2 = 180^\circ - 53.13^\circ = 126.87^\circ$
Final answers: $\theta = 53.13^\circ, 126.87^\circ$
53.13^\circ, 126.87^\circ

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