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What are the solutions of the equation sin^2(x) - sin(x) = 0?
What are the solutions of the equation sin^2(x) - sin(x) = 0?
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Practice Questions
1 question
Q1
What are the solutions of the equation sin^2(x) - sin(x) = 0?
x = nπ
x = nπ + π/2
x = nπ + 2π
x = nπ + π
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Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.
Questions & Step-by-step Solutions
1 item
Q
Q: What are the solutions of the equation sin^2(x) - sin(x) = 0?
Solution:
Factoring gives sin(x)(sin(x) - 1) = 0, so sin(x) = 0 or sin(x) = 1. Thus, x = nπ or x = π/2 + 2nπ.
Steps: 8
Show Steps
Step 1: Start with the equation sin^2(x) - sin(x) = 0.
Step 2: Notice that this equation can be factored. Rewrite it as sin(x)(sin(x) - 1) = 0.
Step 3: Set each factor equal to zero. First, set sin(x) = 0.
Step 4: Solve sin(x) = 0. The solutions are x = nπ, where n is any integer.
Step 5: Now, set the second factor equal to zero: sin(x) - 1 = 0.
Step 6: Solve sin(x) - 1 = 0. This gives sin(x) = 1.
Step 7: The solutions for sin(x) = 1 are x = π/2 + 2nπ, where n is any integer.
Step 8: Combine the solutions from both factors. The final solutions are x = nπ or x = π/2 + 2nπ.
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