Trigonometry question

Question

Find the solution set of each equation in the interval : 0 ≤ x < 2 : 4 cos 2x = 2

a. { π/3, 5π/3}

b. { π/6, 5π/6, 7π/6, 11π/6}

c. { π/3, 11π/6}

d. { π/3, 2π/3, 4π/3, 5π/3}

Answer 1

1. Solve for all the possible angles.
2. Solve for the corresponding x values.

4 cos 2x = 2

cos 2x = 1/2

cos θ = 1/2

θ = π/3 or 5π/3

Now, 7π/3 is coterminal with π/3, and 11π/3 is coterminal with 5π/3. Altogether we have 4 angles to consider that will yield solutions within the given range of x values.

2x₁=π/3 2x₂=5π/3 2x₃=7π/3 2x₄=11π/3

x₁=π/6 x₂=5π/6 x₃=7π/6 x₄=11π/6

ANSWER: B