Trigonometric function graph
I tried to tweak a trigonometric function in Wolframalpha to kinda transform the sin function into a rounded square function. Please see screenshot here: Wolframaplpha graph.
First function looks good for y=1, but I'd prefer to have a higher slope for y=0, just as the second function is.
Is there an elegant formula to achieve that with a periodic function , like sin?
Cheers!
trigonometry
asked Nov 30 at 8:45
Dani Dobre
11
add a comment |
I tried to tweak a trigonometric function in Wolframalpha to kinda transform the sin function into a rounded square function. Please see screenshot here: Wolframaplpha graph.
First function looks good for y=1, but I'd prefer to have a higher slope for y=0, just as the second function is.
Is there an elegant formula to achieve that with a periodic function , like sin?
Cheers!
trigonometry
asked Nov 30 at 8:45
Dani Dobre
11
add a comment |
I tried to tweak a trigonometric function in Wolframalpha to kinda transform the sin function into a rounded square function. Please see screenshot here: Wolframaplpha graph.
First function looks good for y=1, but I'd prefer to have a higher slope for y=0, just as the second function is.
Is there an elegant formula to achieve that with a periodic function , like sin?
Cheers!
trigonometry
asked Nov 30 at 8:45
Dani Dobre
11
I tried to tweak a trigonometric function in Wolframalpha to kinda transform the sin function into a rounded square function. Please see screenshot here: Wolframaplpha graph.
First function looks good for y=1, but I'd prefer to have a higher slope for y=0, just as the second function is.
Is there an elegant formula to achieve that with a periodic function , like sin?
Cheers!
trigonometry
trigonometry
asked Nov 30 at 8:45
Dani Dobre
11
asked Nov 30 at 8:45
Dani Dobre
11
asked Nov 30 at 8:45
Dani Dobre
11
asked Nov 30 at 8:45
Dani Dobre
11
asked Nov 30 at 8:45
Dani Dobre
11
11
add a comment |
add a comment |
3 Answers
3
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oldest
votes
Here's the Fourier synthesis of an unnormalized square wave, cut off at term $n$. Adjust $n$ to your needs.
$f(x) = sumlimits_{i=1, 3, 5 ldots}^n {1 over i} sin (i x)$
answered Nov 30 at 9:11
David G. Stork
9,54721232
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
add a comment |
A Fourier series will work here, it is a linear combination of individual sin functions with different periods and amplitudes. For example, for the square function
$$
f(x) = frac{4}{pi}sum_{k = 0}^{+infty}frac{1}{2 k + 1}sinleft((2k + 1)frac{x}{2}right)
$$
If you truncate the series at a given $k$ you will be successively better approximations, here's a graph
answered Nov 30 at 9:16
caverac
13k21028
add a comment |
I have found the answer. First, I was thinking why is 1.8 so special, but realized it is close to pi/2, so I've changed 1.8 to pi/2. Then, I thought I should try sin(sin(sin(x)...
Here's the graph:
https://www.wolframalpha.com/input/?i=plot+sin(sin(x)*pi%2F2)+plot+sin(sin(sin(x)*pi%2F2)*pi%2F2)
answered Nov 30 at 13:07
Dani Dobre
11
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
Here's the Fourier synthesis of an unnormalized square wave, cut off at term $n$. Adjust $n$ to your needs.
$f(x) = sumlimits_{i=1, 3, 5 ldots}^n {1 over i} sin (i x)$
answered Nov 30 at 9:11
David G. Stork
9,54721232
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
add a comment |
Here's the Fourier synthesis of an unnormalized square wave, cut off at term $n$. Adjust $n$ to your needs.
$f(x) = sumlimits_{i=1, 3, 5 ldots}^n {1 over i} sin (i x)$
answered Nov 30 at 9:11
David G. Stork
9,54721232
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
add a comment |
Here's the Fourier synthesis of an unnormalized square wave, cut off at term $n$. Adjust $n$ to your needs.
$f(x) = sumlimits_{i=1, 3, 5 ldots}^n {1 over i} sin (i x)$
answered Nov 30 at 9:11
David G. Stork
9,54721232
Here's the Fourier synthesis of an unnormalized square wave, cut off at term $n$. Adjust $n$ to your needs.
$f(x) = sumlimits_{i=1, 3, 5 ldots}^n {1 over i} sin (i x)$
answered Nov 30 at 9:11
David G. Stork
9,54721232
answered Nov 30 at 9:11
David G. Stork
9,54721232
answered Nov 30 at 9:11
David G. Stork
9,54721232
answered Nov 30 at 9:11
David G. Stork
9,54721232
9,54721232
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
add a comment |
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
I am using the function to simulate the air bubble movement in an Android "level" app. Your response is great, but the amplitude of the horizontal part makes the air bubble wobble noticeably. Is there another way to stretch the horizontal part of the sin(sin(x)*1.8) graph?
– Dani Dobre
Nov 30 at 12:27
add a comment |
A Fourier series will work here, it is a linear combination of individual sin functions with different periods and amplitudes. For example, for the square function
$$
f(x) = frac{4}{pi}sum_{k = 0}^{+infty}frac{1}{2 k + 1}sinleft((2k + 1)frac{x}{2}right)
$$
If you truncate the series at a given $k$ you will be successively better approximations, here's a graph
answered Nov 30 at 9:16
caverac
13k21028
add a comment |
A Fourier series will work here, it is a linear combination of individual sin functions with different periods and amplitudes. For example, for the square function
$$
f(x) = frac{4}{pi}sum_{k = 0}^{+infty}frac{1}{2 k + 1}sinleft((2k + 1)frac{x}{2}right)
$$
If you truncate the series at a given $k$ you will be successively better approximations, here's a graph
answered Nov 30 at 9:16
caverac
13k21028
add a comment |
A Fourier series will work here, it is a linear combination of individual sin functions with different periods and amplitudes. For example, for the square function
$$
f(x) = frac{4}{pi}sum_{k = 0}^{+infty}frac{1}{2 k + 1}sinleft((2k + 1)frac{x}{2}right)
$$
If you truncate the series at a given $k$ you will be successively better approximations, here's a graph
answered Nov 30 at 9:16
caverac
13k21028
A Fourier series will work here, it is a linear combination of individual sin functions with different periods and amplitudes. For example, for the square function
$$
f(x) = frac{4}{pi}sum_{k = 0}^{+infty}frac{1}{2 k + 1}sinleft((2k + 1)frac{x}{2}right)
$$
If you truncate the series at a given $k$ you will be successively better approximations, here's a graph
answered Nov 30 at 9:16
caverac
13k21028
answered Nov 30 at 9:16
caverac
13k21028
answered Nov 30 at 9:16
caverac
13k21028
answered Nov 30 at 9:16
caverac
13k21028
13k21028
add a comment |
add a comment |
I have found the answer. First, I was thinking why is 1.8 so special, but realized it is close to pi/2, so I've changed 1.8 to pi/2. Then, I thought I should try sin(sin(sin(x)...
Here's the graph:
https://www.wolframalpha.com/input/?i=plot+sin(sin(x)*pi%2F2)+plot+sin(sin(sin(x)*pi%2F2)*pi%2F2)
answered Nov 30 at 13:07
Dani Dobre
11
add a comment |
I have found the answer. First, I was thinking why is 1.8 so special, but realized it is close to pi/2, so I've changed 1.8 to pi/2. Then, I thought I should try sin(sin(sin(x)...
Here's the graph:
https://www.wolframalpha.com/input/?i=plot+sin(sin(x)*pi%2F2)+plot+sin(sin(sin(x)*pi%2F2)*pi%2F2)
answered Nov 30 at 13:07
Dani Dobre
11
add a comment |
I have found the answer. First, I was thinking why is 1.8 so special, but realized it is close to pi/2, so I've changed 1.8 to pi/2. Then, I thought I should try sin(sin(sin(x)...
Here's the graph:
https://www.wolframalpha.com/input/?i=plot+sin(sin(x)*pi%2F2)+plot+sin(sin(sin(x)*pi%2F2)*pi%2F2)
answered Nov 30 at 13:07
Dani Dobre
11
I have found the answer. First, I was thinking why is 1.8 so special, but realized it is close to pi/2, so I've changed 1.8 to pi/2. Then, I thought I should try sin(sin(sin(x)...
Here's the graph:
https://www.wolframalpha.com/input/?i=plot+sin(sin(x)*pi%2F2)+plot+sin(sin(sin(x)*pi%2F2)*pi%2F2)
answered Nov 30 at 13:07
Dani Dobre
11
answered Nov 30 at 13:07
Dani Dobre
11
answered Nov 30 at 13:07
Dani Dobre
11
answered Nov 30 at 13:07
Dani Dobre
11
11
add a comment |
add a comment |
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