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

Step 1: Start with the given equation.
$5 \sin \theta = 4$

Step 2: Divide both sides by 5.
$\sin \theta = \frac{4}{5} = 0.8$

Step 3: $\sin \theta = 0.8 > 0$, so solutions are in the first and second quadrants between $0^\circ$ and $360^\circ$.

Step 4: Reference angle $\alpha = \sin^{-1}(0.8)$.
$\alpha \approx 53.13^\circ$

Step 5: First quadrant solution.
$\theta_1 = 53.13^\circ$

Step 6: 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