Angle subtended by arc. [on hold]
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consider the segment of a circle. I know the arc length and the width of the segment (the line connecting the end points of the arc). I donot know the radius. But angle subtended varies between 0 and 180 degrees. how can i find the radius of the arc for various width of the segment while the arc length remains constant ?
trigonometry mathematical-modeling
asked Nov 20 at 14:43
gokul prassad
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put on hold as off-topic by user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
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consider the segment of a circle. I know the arc length and the width of the segment (the line connecting the end points of the arc). I donot know the radius. But angle subtended varies between 0 and 180 degrees. how can i find the radius of the arc for various width of the segment while the arc length remains constant ?
trigonometry mathematical-modeling
asked Nov 20 at 14:43
gokul prassad
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18
add a comment |
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down vote
favorite
up vote
0
down vote
favorite
consider the segment of a circle. I know the arc length and the width of the segment (the line connecting the end points of the arc). I donot know the radius. But angle subtended varies between 0 and 180 degrees. how can i find the radius of the arc for various width of the segment while the arc length remains constant ?
trigonometry mathematical-modeling
asked Nov 20 at 14:43
gokul prassad
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
consider the segment of a circle. I know the arc length and the width of the segment (the line connecting the end points of the arc). I donot know the radius. But angle subtended varies between 0 and 180 degrees. how can i find the radius of the arc for various width of the segment while the arc length remains constant ?
trigonometry mathematical-modeling
trigonometry mathematical-modeling
asked Nov 20 at 14:43
gokul prassad
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:43
gokul prassad
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:43
gokul prassad
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 14:43
gokul prassad
1
asked Nov 20 at 14:43
gokul prassad
1
1
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
gokul prassad is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos 2 days ago
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – user10354138, user302797, José Carlos Santos, ancientmathematician, Rebellos
If this question can be reworded to fit the rules in the help center, please edit the question.
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18
add a comment |
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18
add a comment |
1 Answer
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For an arc of aperture $2alpha$ and unit radius (hence angle and arc length are equal), the chord length is $2sinalpha$.
Hence, the ratio of the arc over the chord is
$$frac ac=frac{sinalpha}{alpha}=text{sinc }alpha.$$
When you know this ratio, you can obtain the half-angle by
$$alpha=text{sinc}^{-1}frac ac,$$ but this inverse function is not commonly available and you should solve the equation numerically.
Then
$$r=frac aalpha.$$
For small angles, you can use
$$text{sinc }alphaapprox 1-frac{alpha^2}6+frac{alpha^4}{120}$$ and solve the biquadratic equation.
answered Nov 20 at 15:18
Yves Daoust
121k668216
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
For an arc of aperture $2alpha$ and unit radius (hence angle and arc length are equal), the chord length is $2sinalpha$.
Hence, the ratio of the arc over the chord is
$$frac ac=frac{sinalpha}{alpha}=text{sinc }alpha.$$
When you know this ratio, you can obtain the half-angle by
$$alpha=text{sinc}^{-1}frac ac,$$ but this inverse function is not commonly available and you should solve the equation numerically.
Then
$$r=frac aalpha.$$
For small angles, you can use
$$text{sinc }alphaapprox 1-frac{alpha^2}6+frac{alpha^4}{120}$$ and solve the biquadratic equation.
answered Nov 20 at 15:18
Yves Daoust
121k668216
add a comment |
up vote
0
down vote
For an arc of aperture $2alpha$ and unit radius (hence angle and arc length are equal), the chord length is $2sinalpha$.
Hence, the ratio of the arc over the chord is
$$frac ac=frac{sinalpha}{alpha}=text{sinc }alpha.$$
When you know this ratio, you can obtain the half-angle by
$$alpha=text{sinc}^{-1}frac ac,$$ but this inverse function is not commonly available and you should solve the equation numerically.
Then
$$r=frac aalpha.$$
For small angles, you can use
$$text{sinc }alphaapprox 1-frac{alpha^2}6+frac{alpha^4}{120}$$ and solve the biquadratic equation.
answered Nov 20 at 15:18
Yves Daoust
121k668216
add a comment |
up vote
0
down vote
up vote
0
down vote
For an arc of aperture $2alpha$ and unit radius (hence angle and arc length are equal), the chord length is $2sinalpha$.
Hence, the ratio of the arc over the chord is
$$frac ac=frac{sinalpha}{alpha}=text{sinc }alpha.$$
When you know this ratio, you can obtain the half-angle by
$$alpha=text{sinc}^{-1}frac ac,$$ but this inverse function is not commonly available and you should solve the equation numerically.
Then
$$r=frac aalpha.$$
For small angles, you can use
$$text{sinc }alphaapprox 1-frac{alpha^2}6+frac{alpha^4}{120}$$ and solve the biquadratic equation.
answered Nov 20 at 15:18
Yves Daoust
121k668216
For an arc of aperture $2alpha$ and unit radius (hence angle and arc length are equal), the chord length is $2sinalpha$.
Hence, the ratio of the arc over the chord is
$$frac ac=frac{sinalpha}{alpha}=text{sinc }alpha.$$
When you know this ratio, you can obtain the half-angle by
$$alpha=text{sinc}^{-1}frac ac,$$ but this inverse function is not commonly available and you should solve the equation numerically.
Then
$$r=frac aalpha.$$
For small angles, you can use
$$text{sinc }alphaapprox 1-frac{alpha^2}6+frac{alpha^4}{120}$$ and solve the biquadratic equation.
answered Nov 20 at 15:18
Yves Daoust
121k668216
answered Nov 20 at 15:18
Yves Daoust
121k668216
answered Nov 20 at 15:18
Yves Daoust
121k668216
answered Nov 20 at 15:18
Yves Daoust
121k668216
121k668216
add a comment |
add a comment |
What do you know about the relationship between radius, arc and chord length to solve this problem? Please share your thoughts to avoid down votes.
– Phil H
Nov 20 at 15:18