Question

If 4sinθ−8=−10, where 0≤θ<2π, what are the values of θ? List your answers as exact answers in terms of π, separated by a comma if necessary.

a) π/6, 5π/6
b) 2π/3, 4π/3
c) π/3, 2π/3
d) 5π/4, 7π/4

Answer 1

The values of θ that satisfy the equation 4sinθ−8=−10, where 0≤θ<2π, are π/6 and 5π/6.

Step-by-step explanation:

To solve the equation 4sinθ−8=−10, we need to isolate the sinθ term. First, we add 8 to both sides of the equation: 4sinθ = -2. Then, we divide both sides by 4 to get sinθ = -1/2. Since the range for θ is 0≤θ<2π, we need to find the angles within this range that have a sine of -1/2.

The angles θ that satisfy sinθ = -1/2 are π/6 and 5π/6. Therefore, the values of θ that satisfy the given equation are a) π/6, 5π/6.