Determine the values of x that satisfy the equation sin(2x) = 0.

Determine the values of x that satisfy the equation sin(2x) = 0.

Correct Answer: x = nπ/2, where n is any integer

Step 1: Understand the equation sin(2x) = 0. This means we need to find the angles where the sine function equals zero.
Step 2: Recall that the sine function equals zero at integer multiples of π. Specifically, sin(θ) = 0 when θ = nπ, where n is any integer.
Step 3: Since we have sin(2x) = 0, we set 2x equal to nπ: 2x = nπ.
Step 4: To solve for x, divide both sides of the equation by 2: x = nπ/2.
Step 5: The final solution is x = nπ/2, where n can be any integer (like 0, 1, -1, 2, -2, etc.).

Trigonometric Equations – The question tests the understanding of solving trigonometric equations, specifically using the sine function and its periodic properties.
Periodicity of Sine Function – It assesses knowledge of the periodic nature of the sine function, where sin(θ) = 0 at integer multiples of π.