What are the solutions of the equation sin(2x) = 0?

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Question: What are the solutions of the equation sin(2x) = 0?

Options:

Correct Answer: x = nπ/2

Solution:

sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.

What are the solutions of the equation sin(2x) = 0?

What are the solutions of the equation sin(2x) = 0?

Step 1: Understand the equation sin(2x) = 0. This means we want to find the values of x where the sine of 2x equals zero.
Step 2: Recall that the sine function equals zero at integer multiples of π (pi). This means sin(θ) = 0 when θ = nπ, where n is any integer (n ∈ Z).
Step 3: Set 2x equal to nπ. So, we write the equation as 2x = nπ.
Step 4: Solve for x by dividing both sides of the equation by 2. This gives us x = nπ/2.
Step 5: Remember that n can be any integer, so the solutions are x = nπ/2 for n ∈ Z.

Trigonometric Equations – The question tests the understanding of solving trigonometric equations, specifically using the sine function and its properties.
Periodic Solutions – It assesses the ability to recognize that sine functions have periodic solutions, leading to multiple valid answers.