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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?
General Solution of sin x=0: 0, pi or 2pi?
- Thread starter cscott
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In summary, the general solution of sin x = 0 can be written as k*pi, where k is any non-negative integer. This includes solutions at 0, pi, 2pi, etc. Negative integers can also be used as coefficients to obtain solutions at negative multiples of pi.
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amcavoy
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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
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cscott
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I feel dumb for asking now
0 + pi * k
0 + pi * k
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amcavoy
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Yes, for all non-negative integer values of k.cscott said:
Alex
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cscott
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apmcavoy said:
Doesn't it still work for negative integers or am I missing something?
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TD
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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
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cscott
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Thank you kind sirs.
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TD
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You're welcome
FAQ: General Solution of sin x=0: 0, pi or 2pi?
What does "General Solution of sin x=0: 0, pi or 2pi" mean?
The general solution of sin x=0 refers to the set of all possible values of x that satisfy the equation sin x=0. In this case, the solution set includes 0, pi, and 2pi, as these are all values of x that make sin x equal to 0.
Why are there multiple solutions for sin x=0?
Since the sine function is periodic, it repeats itself after every 2pi radians (or 360 degrees). Therefore, there are multiple values of x that make sin x=0, and these values are spaced out at intervals of 2pi.
How can I find the general solution for sin x=0?
To find the general solution for sin x=0, you can use basic trigonometric identities and properties to manipulate the equation and solve for x. In this case, you can divide both sides by sin x and use the fact that sin 0=0, sin pi=0, and sin 2pi=0 to find all possible values of x.
Can the general solution of sin x=0 be expressed in radians and degrees?
Yes, the general solution of sin x=0 can be expressed in both radians and degrees. Radians are the preferred unit of measurement for angles in mathematics, while degrees are commonly used in everyday life. To convert from radians to degrees, you can use the formula: degrees = (radians * 180) / pi.
Are there any other solutions for sin x=0 besides 0, pi, and 2pi?
No, there are no other solutions for sin x=0 besides 0, pi, and 2pi. These three values make up the entire solution set for this equation. However, if you are looking for solutions in a specific range or interval, there may be other values of x that make sin x=0 within that range.