Question

Which of the following are solutions to the following equation where 0≤θ<2π

2 cos (πθ)=1

a. 1/6
b. 5/6
c. 7/6
d. 13/6
e. 15/6
f. 17/6

Answer 1

To find the solutions to the equation 2 cos (πθ) = 1, divide both sides by 2 and then take the inverse cosine to solve for θ.

Step-by-step explanation:

To find the solutions to the equation 2 cos (πθ) = 1, where 0≤θ<2π, we can use the inverse cosine function to isolate θ.

1. Start by dividing both sides of the equation by 2: cos (πθ) = 1/2.
2. Take the inverse cosine of both sides to solve for θ. This will give you two solutions: πθ = ±π/3.
3. Divide both sides of the new equation by π: θ = ±(π/3π).
4. Simplify the expression: θ = ±1/3.

So, the solutions to the equation are θ = 1/3 and θ = -1/3.