Mixing
Combination of function's roots question
I have a trig function $$sin(frac{pi}{3}x)$$ with roots at 0, 3, 6, 9. I also have a function $$sin(frac{pi}{4}x)$$ with roots at 0, 4, 8, 12. I am looking for a generalized way to combine them as one function in a way that preserves their roots (and doesn't add any), regardless of what happens everywhere else. This is more of a question of the method rather than a specific answer. All creative answers are much appreciated!
trigonometry combinations roots
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
add a comment |
I have a trig function $$sin(frac{pi}{3}x)$$ with roots at 0, 3, 6, 9. I also have a function $$sin(frac{pi}{4}x)$$ with roots at 0, 4, 8, 12. I am looking for a generalized way to combine them as one function in a way that preserves their roots (and doesn't add any), regardless of what happens everywhere else. This is more of a question of the method rather than a specific answer. All creative answers are much appreciated!
trigonometry combinations roots
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58
add a comment |
I have a trig function $$sin(frac{pi}{3}x)$$ with roots at 0, 3, 6, 9. I also have a function $$sin(frac{pi}{4}x)$$ with roots at 0, 4, 8, 12. I am looking for a generalized way to combine them as one function in a way that preserves their roots (and doesn't add any), regardless of what happens everywhere else. This is more of a question of the method rather than a specific answer. All creative answers are much appreciated!
trigonometry combinations roots
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
I have a trig function $$sin(frac{pi}{3}x)$$ with roots at 0, 3, 6, 9. I also have a function $$sin(frac{pi}{4}x)$$ with roots at 0, 4, 8, 12. I am looking for a generalized way to combine them as one function in a way that preserves their roots (and doesn't add any), regardless of what happens everywhere else. This is more of a question of the method rather than a specific answer. All creative answers are much appreciated!
trigonometry combinations roots
trigonometry combinations roots
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
edited Nov 22 '18 at 1:56
Ryan Shesler
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
asked Nov 22 '18 at 1:31
Ryan SheslerRyan Shesler
86
86
isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58
add a comment |
isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58
isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58
add a comment |
1 Answer
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Just multiply the two functions. You will get roots only when you have a root of either (or both) of those functions. Also see my comment about the roots of the cosine function.
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
add a comment |
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Just multiply the two functions. You will get roots only when you have a root of either (or both) of those functions. Also see my comment about the roots of the cosine function.
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
add a comment |
Just multiply the two functions. You will get roots only when you have a root of either (or both) of those functions. Also see my comment about the roots of the cosine function.
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
add a comment |
Just multiply the two functions. You will get roots only when you have a root of either (or both) of those functions. Also see my comment about the roots of the cosine function.
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
Just multiply the two functions. You will get roots only when you have a root of either (or both) of those functions. Also see my comment about the roots of the cosine function.
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
answered Nov 22 '18 at 1:52
AndreiAndrei
11.4k21026
11.4k21026
add a comment |
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isn't $12$ a root for the first function?
– Siong Thye Goh
Nov 22 '18 at 1:34
yes but the goal is to find a function with roots 0, 3, 4, 6, 8, 9, 12... or use the same method with any two functions like these
– Ryan Shesler
Nov 22 '18 at 1:41
$cos 0=1$, $cospi=-1$, ... None of those are roots
– Andrei
Nov 22 '18 at 1:49
That was a typo I meant sine. Sorry for the confusion but thanks for the answer!
– Ryan Shesler
Nov 22 '18 at 1:58