- #1
cscott
- 778
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For the general solution of sin x = 0, must you have a solution using 0, pi and 2pi (ie. pi + 2pi * k, 2pi + 2pi * k, ...) or does using pi suffice?
General Solution of sin x=0: 0, pi or 2pi?
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- Thread starter cscott
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Discussion Overview
The discussion centers on the general solution for the equation sin x = 0, exploring whether the solutions should include 0, π, and 2π, or if using just π is sufficient. The conversation involves mathematical reasoning and clarification of general solutions in trigonometric contexts.
Discussion Character
- Mathematical reasoning, Conceptual clarification, Debate/contested
Main Points Raised
- Some participants propose that the general solution can be expressed as kπ, where k is any integer, which would include all solutions such as 0, π, and 2π.
- Others argue that specifying 0, π, and 2π is necessary for clarity in writing the general solution.
- A participant questions whether negative integer values of k also yield valid solutions, suggesting that the inclusion of negative integers may be overlooked.
- There is a suggestion that using k = 0, k = 1, and k = 2 provides the specific solutions of 0, π, and 2π, respectively.
Areas of Agreement / Disagreement
Participants express differing views on whether the general solution should explicitly include 0, π, and 2π, or if stating kπ suffices. The discussion remains unresolved regarding the necessity of including specific values versus a more general form.
Contextual Notes
Some assumptions about the integer values of k and their implications for the general solution are not fully explored, leaving room for interpretation regarding the completeness of the solution set.
- #2
amcavoy
- 663
- 0
Sin(x) is zero when x is 0, pi, 2pi, etc. What does this tell you in terms of writing a general solution? Pay attention to the coefficients.cscott said:
Alex
- #3
cscott
- 778
- 1
I feel dumb for asking now
0 + pi * k
0 + pi * k
- #4
amcavoy
- 663
- 0
Yes, for all non-negative integer values of k.cscott said:
Alex
- #5
cscott
- 778
- 1
apmcavoy said:
Doesn't it still work for negative integers or am I missing something?
Last edited:
- #6
TD
Homework Helper
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If you use k*pi with k an integer, you have all of your solutions.cscott said:
Since, choose k = 0 to find the solution 0, use k = 1 to find the solution pi and use k = 2 to find 2*pi. Of course, all (positive and negative) multiples or 2*pi are allowed as well
- #7
cscott
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Thank you kind sirs.
- #8
TD
Homework Helper
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You're welcome
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