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What are the solutions of the equation sin(2x) = 0?
What are the solutions of the equation sin(2x) = 0?
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Practice Questions
1 question
Q1
What are the solutions of the equation sin(2x) = 0?
x = nπ/2
x = nπ
x = nπ + π/2
x = nπ + π
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sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the solutions of the equation sin(2x) = 0?
Solution:
sin(2x) = 0 implies 2x = nπ, thus x = nπ/2 for n ∈ Z.
Steps: 5
Show Steps
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.
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