MATH SOLVE

4 months ago

Q:
# Need help finding 3 and 6 in decimal form

Accepted Solution

A:

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 kStep-by-step explanation:3. Divide by 5 to get ... sin(3θ) = -2/5Use the inverse sine function to determine 3θ: 3θ = arcsin(-2/5) ≈ -0.411517 or 3.553109 . . . . . 3rd and 4th quadrant anglesEach of these answers repeats every 2π, so ... 3θ = {-0.411517, 3.553109} +2kπ . . . . . for any integer kDividing by 3 gives ... θ = {-0.137172, 1.184370} +2kπ/3 . . . . . for any integer k__6. Solved the same way. sin(πθ/2) = 1/4 (π/2)θ = arcsin(1/4) ≈ {0.252680, 2.888912} +2kπ . . . . for any integer kMultiplying by 2/π gives ... θ ≈ {0.160861, 1.839139} +4k . . . . for any integer k_____Make sure your calculator is in radians mode for the arcsin function.