Answer:
3. θ ≈ -0.137172 or 1.184370 . . . . +(2π/3)k for any integer k
6. θ ≈ 0.160861 or 1.839139 . . . . +4k for any integer k
Step-by-step explanation:
3. Divide by 5 to get ...
sin(3θ) = -2/5
Use the inverse sine function to determine 3θ:
3θ = arcsin(-2/5) ≈ -0.411517 or 3.553109 . . . . . 3rd and 4th quadrant angles
Each of these answers repeats every 2π, so ...
3θ = {-0.411517, 3.553109} +2kπ . . . . . for any integer k
Dividing by 3 gives ...
θ = {-0.137172, 1.184370} +2kπ/3 . . . . . for any integer k
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6. Solved the same way.
sin(πθ/2) = 1/4
(π/2)θ = arcsin(1/4) ≈ {0.252680, 2.888912} +2kπ . . . . for any integer k
Multiplying by 2/π gives ...
θ ≈ {0.160861, 1.839139} +4k . . . . for any integer k
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Make sure your calculator is in radians mode for the arcsin function.
