Question

What values for θ (0 ≤ θ ≤ 2π) satisfy the equation?

2 sinθ cos θ + √2 cos θ = 0

A. pi/2, 3pi/4, 3pi/2, 7pi/4

B. pi/2, 3pi/4, 5pi/2, 7pi/4

C. pi/2, 5pi/4, 3pi/2, 7pi/4

D. pi/2, 5pi/4, 3pi/4, 7pi/4

Answer 1

Factorizing the equation, we have:

cos θ (2sin θ + √2) = 0

Either cos θ = 0 or 2sin θ + √2 = 0.

If cos θ = 0, then θ = π/2 or 3π/2.

If 2sin θ + √2 = 0, then sin θ = - √2/2, which occurs at 3π/4 and 5π/4.

Therefore, the values of θ that satisfy the equation are π/2, 3π/4, 5π/4, and 3π/2, which is answer choice B.