Question

For what values of θ is sin^2(θ) > 1/2?

a) θ = nπ, where n is an even integer
b) θ = (2n + 1)π/4, where n is an integer
c) θ = nπ/2, where n is an odd integer
d) θ = (2n + 1)π/2, where n is an integer

Answer 1

The values of θ that satisfy the inequality sin^2(θ) > 1/2 are given by θ = (2n + 1)π/4, where n is an integer.

Step-by-step explanation:

The inequality sin^2(θ) > 1/2 can be rewritten as sin(θ) > √(1/2). Since sin(θ) is positive in Quadrant I and Quadrant II, we can focus on those quadrants when determining the values of θ that satisfy the inequality.

Option b) θ = (2n + 1)π/4, where n is an integer, satisfies the inequality sin^2(θ) > 1/2 in Quadrant I. For example, when n = 0, θ = π/4 and sin^2(θ) = 1/2, which is greater than 1/2.

Therefore, the correct answer is b) θ = (2n + 1)π/4, where n is an integer.