Question

Determine the exact value of θ in the following equation if 0≤θ<2π.
8cos² θ+2=8

Answer 1

To determine the value of θ, subtract 2 from both sides, divide by 8, take the square root, and find the inverse cosine.

Step-by-step explanation:

To determine the exact value of θ in the equation 8cos² θ + 2 = 8, we need to isolate the cosine term and solve for θ. Here are the steps:

1. Subtract 2 from both sides to get 8cos² θ = 6.
2. Divide both sides by 8 to get cos² θ = 0.75.
3. Take the square root of both sides to get cos θ = ±√0.75.
4. Since 0≤θ<2π, the value of cos θ will be positive in the first and fourth quadrants.
5. Using a calculator, find the inverse cosine of √0.75, which is approximately 0.841 radians or 48.19 degrees.

Therefore, the exact value of θ in the equation is approximately 0.841 radians or 48.19 degrees.