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Find the general solution of the equation cos(2x) = 0.
Find the general solution of the equation cos(2x) = 0.
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Practice Questions
1 question
Q1
Find the general solution of the equation cos(2x) = 0.
x = (2n+1)π/4
x = nπ/2
x = (2n+1)π/2
x = nπ
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The general solution is x = (2n+1)π/4, where n is any integer.
Questions & Step-by-step Solutions
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Q
Q: Find the general solution of the equation cos(2x) = 0.
Solution:
The general solution is x = (2n+1)π/4, where n is any integer.
Steps: 5
Show Steps
Step 1: Start with the equation cos(2x) = 0.
Step 2: Recall that cosine equals zero at specific angles. The angles where cos(θ) = 0 are θ = (2n + 1)π/2, where n is any integer.
Step 3: Set 2x equal to the angles where cosine is zero: 2x = (2n + 1)π/2.
Step 4: Solve for x by dividing both sides of the equation by 2: x = (2n + 1)π/4.
Step 5: Write the final answer, which is the general solution: x = (2n + 1)π/4, where n is any integer.
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