Aryabhata's sine approximation : Conversion for use with interval of $[-pi,pi]$
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There's this sine approximation (mentioned in title) which works over the interval $[0, pi]$:
$$
sin x approx frac{16x(pi-x)} {5pi^2-4x(pi-x)}
$$
With little changes it can be put work over the interval $[-pi, 0]$:
$$
sin x approx frac{-16x(-pi-x)} {5pi^2-4x(-pi-x)}
$$
Approximation results as - https://www.desmos.com/calculator/cvoewagqer
Is there any change to join these two formulas into one equation to work in range $[-pi, pi]$? If there's ... how?
Source:
P.Giblin's paper: https://www.liverpool.ac.uk/~pjgiblin/papers/sine-approx.pdf
trigonometry polynomials approximation
asked Nov 24 '18 at 12:03
Juha PJuha P
112
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add a comment |
$begingroup$
There's this sine approximation (mentioned in title) which works over the interval $[0, pi]$:
$$
sin x approx frac{16x(pi-x)} {5pi^2-4x(pi-x)}
$$
With little changes it can be put work over the interval $[-pi, 0]$:
$$
sin x approx frac{-16x(-pi-x)} {5pi^2-4x(-pi-x)}
$$
Approximation results as - https://www.desmos.com/calculator/cvoewagqer
Is there any change to join these two formulas into one equation to work in range $[-pi, pi]$? If there's ... how?
Source:
P.Giblin's paper: https://www.liverpool.ac.uk/~pjgiblin/papers/sine-approx.pdf
trigonometry polynomials approximation
asked Nov 24 '18 at 12:03
Juha PJuha P
112
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Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
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– José Carlos Santos
Nov 24 '18 at 12:06
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@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53
add a comment |
$begingroup$
There's this sine approximation (mentioned in title) which works over the interval $[0, pi]$:
$$
sin x approx frac{16x(pi-x)} {5pi^2-4x(pi-x)}
$$
With little changes it can be put work over the interval $[-pi, 0]$:
$$
sin x approx frac{-16x(-pi-x)} {5pi^2-4x(-pi-x)}
$$
Approximation results as - https://www.desmos.com/calculator/cvoewagqer
Is there any change to join these two formulas into one equation to work in range $[-pi, pi]$? If there's ... how?
Source:
P.Giblin's paper: https://www.liverpool.ac.uk/~pjgiblin/papers/sine-approx.pdf
trigonometry polynomials approximation
asked Nov 24 '18 at 12:03
Juha PJuha P
112
$endgroup$
There's this sine approximation (mentioned in title) which works over the interval $[0, pi]$:
$$
sin x approx frac{16x(pi-x)} {5pi^2-4x(pi-x)}
$$
With little changes it can be put work over the interval $[-pi, 0]$:
$$
sin x approx frac{-16x(-pi-x)} {5pi^2-4x(-pi-x)}
$$
Approximation results as - https://www.desmos.com/calculator/cvoewagqer
Is there any change to join these two formulas into one equation to work in range $[-pi, pi]$? If there's ... how?
Source:
P.Giblin's paper: https://www.liverpool.ac.uk/~pjgiblin/papers/sine-approx.pdf
trigonometry polynomials approximation
trigonometry polynomials approximation
asked Nov 24 '18 at 12:03
Juha PJuha P
112
asked Nov 24 '18 at 12:03
Juha PJuha P
112
edited Nov 24 '18 at 15:29
Juha P
asked Nov 24 '18 at 12:03
Juha PJuha P
112
asked Nov 24 '18 at 12:03
Juha PJuha P
112
asked Nov 24 '18 at 12:03
Juha PJuha P
112
112
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Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Nov 24 '18 at 12:06
$begingroup$
@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53
add a comment |
$begingroup$
Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Nov 24 '18 at 12:06
$begingroup$
@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53
$begingroup$
Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
$begingroup$
Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Nov 24 '18 at 12:06
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Nov 24 '18 at 12:06
$begingroup$
@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53
$begingroup$
@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53
add a comment |
1 Answer
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How about $$ sin x = (text{sgn}(x) 16x(text{sgn}(x)pi-x) / 5pi^2-4x(text{sgn}(x)pi-x))$$
(*This is purely based on the formulae given.)
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
$endgroup$
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
How about $$ sin x = (text{sgn}(x) 16x(text{sgn}(x)pi-x) / 5pi^2-4x(text{sgn}(x)pi-x))$$
(*This is purely based on the formulae given.)
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
$endgroup$
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
add a comment |
$begingroup$
How about $$ sin x = (text{sgn}(x) 16x(text{sgn}(x)pi-x) / 5pi^2-4x(text{sgn}(x)pi-x))$$
(*This is purely based on the formulae given.)
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
$endgroup$
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
add a comment |
$begingroup$
How about $$ sin x = (text{sgn}(x) 16x(text{sgn}(x)pi-x) / 5pi^2-4x(text{sgn}(x)pi-x))$$
(*This is purely based on the formulae given.)
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
$endgroup$
How about $$ sin x = (text{sgn}(x) 16x(text{sgn}(x)pi-x) / 5pi^2-4x(text{sgn}(x)pi-x))$$
(*This is purely based on the formulae given.)
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
answered Nov 24 '18 at 12:54
Yadati KiranYadati Kiran
1,751619
1,751619
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
add a comment |
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
$begingroup$
Thanks, this idea works (after fixing parentheses) as seen in plot - tinyurl.com/y9dsxpb5
$endgroup$
– Juha P
Nov 25 '18 at 6:54
add a comment |
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$begingroup$
Multiply the first one by sign(x) and then replace all the other x's by $|x|?$
$endgroup$
– Ian
Nov 24 '18 at 12:05
$begingroup$
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
$endgroup$
– José Carlos Santos
Nov 24 '18 at 12:06
$begingroup$
@Ian Thanks, this idea works as seen in plot - tinyurl.com/ya9fsgb2
$endgroup$
– Juha P
Nov 25 '18 at 6:53