Question

Solve 19cos θ = 5 cos θ + 14 for all values of θ if θ is measured in radians.

Answer 1

To solve the equation 19cos(θ) = 5cos(θ) + 14 for all values of θ measured in radians, subtract 5cos(θ) from both sides, divide both sides by 14 to isolate cos(θ), and use the inverse cosine function to find the values of θ.

Step-by-step explanation:

To solve the equation 19cos(θ) = 5cos(θ) + 14 for all values of θ measured in radians, we can start by subtracting 5cos(θ) from both sides to get 19cos(θ) - 5cos(θ) = 14. Simplifying this gives us 14cos(θ) = 14. Next, divide both sides by 14 to isolate cos(θ), which gives us cos(θ) = 1. Finally, we can use the inverse cosine function to find the values of θ. Since cos(θ) = 1, θ must equal 0 radians.