Question

Find all solutions of the equation in the interval ((0,2π)) (2cos(θ) - √2 = 0). Write your answer in radians in terms of (π).

A. (θ = π/4)
B. (θ = 3π/4)
C. (θ = 5π/4)
D. (θ = 7π/4)

Answer 1

To find all solutions of the equation 2cos(θ) - √2 = 0 in the interval ((0,2π)), we need to isolate the cosine function and solve for θ. The solutions are θ = π/4, 5π/4, 3π/4, and 7π/4 in radians in terms of π.

Step-by-step explanation:

To find all solutions of the equation 2cos(θ) - √2 = 0 in the interval ((0,2π)), we need to isolate the cosine function and solve for θ.

Step 1: Add √2 to both sides of the equation: 2cos(θ) = √2.

Step 2: Divide both sides of the equation by 2: cos(θ) = √2/2.

Step 3: Find the reference angles that have a cosine value of √2/2. The reference angles are π/4, 7π/4, 3π/4, and 5π/4.

So, the solutions in radians in terms of π are A. (θ = π/4), C. (θ = 5π/4), B. (θ = 3π/4), and D. (θ = 7π/4).