General Solution of sin x=0: 0, pi or 2pi?

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SUMMARY

The general solution for the equation sin x = 0 is expressed as x = kπ, where k is any integer. This encompasses all solutions, including 0, π, and 2π, as well as their negative counterparts. The discussion clarifies that using k as an integer allows for the inclusion of all multiples of π, thus confirming that both positive and negative values are valid solutions. The notation kπ effectively captures the complete set of solutions for sin x = 0.

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  • Understanding of trigonometric functions, specifically sine.
  • Familiarity with the concept of periodicity in trigonometric equations.
  • Knowledge of integer sets and their implications in mathematical solutions.
  • Basic grasp of mathematical notation involving variables and coefficients.
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  • Study the properties of trigonometric functions and their graphs.
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Students and educators in mathematics, particularly those focusing on trigonometry, as well as anyone seeking to deepen their understanding of periodic functions and their solutions.

cscott
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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?
 
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cscott said:
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?
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.

Alex
 
I feel dumb for asking now

0 + pi * k
 
cscott said:
I feel dumb for asking now

0 + pi * k
Yes, for all non-negative integer values of k.

Alex
 
apmcavoy said:
Yes, for all non-negative integer values of k.

Alex

Doesn't it still work for negative integers or am I missing something?
 
Last edited:
cscott said:
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?
If you use k*pi with k an integer, you have all of your solutions.
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 :smile:
 
Thank you kind sirs.
 
You're welcome :smile:
 

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