Step 1: Start with the given equation.
5sinθ=4
Step 2: Divide both sides by 5.
sinθ=54=0.8
Step 3: sinθ=0.8>0, so solutions are in the first and second quadrants between 0∘ and 360∘.
Step 4: Reference angle α=sin−1(0.8).
α≈53.13∘
Step 5: First quadrant solution.
θ1=53.13∘
Step 6: Second quadrant solution.
θ2=180∘−53.13∘=126.87∘
Final answers: θ=53.13∘,126.87∘
53.13^\circ, 126.87^\circ