Coordinates of sector of circle
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I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate the coordinates of the other coordinate of the sector ?
I have quickly mocked up the problem in the image above, please note it is B I am aiming to find.
Angle in rads = 0.262
Radius = 21
Arc length = 5.5
A = (0.5,21)
circle coordinate-systems
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
add a comment |Â
up vote
2
down vote
favorite
I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate the coordinates of the other coordinate of the sector ?
I have quickly mocked up the problem in the image above, please note it is B I am aiming to find.
Angle in rads = 0.262
Radius = 21
Arc length = 5.5
A = (0.5,21)
circle coordinate-systems
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate the coordinates of the other coordinate of the sector ?
I have quickly mocked up the problem in the image above, please note it is B I am aiming to find.
Angle in rads = 0.262
Radius = 21
Arc length = 5.5
A = (0.5,21)
circle coordinate-systems
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate the coordinates of the other coordinate of the sector ?
I have quickly mocked up the problem in the image above, please note it is B I am aiming to find.
Angle in rads = 0.262
Radius = 21
Arc length = 5.5
A = (0.5,21)
circle coordinate-systems
circle coordinate-systems
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
edited Apr 10 '17 at 6:09
Frenzy Li
2,82022345
2,82022345
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
asked Mar 5 '14 at 11:43
Amie-lea Sambrook
213
213
You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23
add a comment |Â
You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23
You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
0
down vote
Same technique as in your other question here.
Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then
$$
x_1 = ; xcos(0.262) + ysin(0.262) \
y_1 = -xsin(0.262) + ycos(0.262) \
$$
This assumes the center is again at $(0,0)$.
edited Apr 13 '17 at 12:21
Community♦
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
Same technique as in your other question here.
Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then
$$
x_1 = ; xcos(0.262) + ysin(0.262) \
y_1 = -xsin(0.262) + ycos(0.262) \
$$
This assumes the center is again at $(0,0)$.
edited Apr 13 '17 at 12:21
Community♦
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
add a comment |Â
up vote
0
down vote
Same technique as in your other question here.
Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then
$$
x_1 = ; xcos(0.262) + ysin(0.262) \
y_1 = -xsin(0.262) + ycos(0.262) \
$$
This assumes the center is again at $(0,0)$.
edited Apr 13 '17 at 12:21
Community♦
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Same technique as in your other question here.
Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then
$$
x_1 = ; xcos(0.262) + ysin(0.262) \
y_1 = -xsin(0.262) + ycos(0.262) \
$$
This assumes the center is again at $(0,0)$.
edited Apr 13 '17 at 12:21
Community♦
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
Same technique as in your other question here.
Let $A = (x,y)$ and let $B= (x_1, y_1)$. Then
$$
x_1 = ; xcos(0.262) + ysin(0.262) \
y_1 = -xsin(0.262) + ycos(0.262) \
$$
This assumes the center is again at $(0,0)$.
edited Apr 13 '17 at 12:21
Community♦
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
edited Apr 13 '17 at 12:21
Community♦
1
1
answered Mar 5 '14 at 12:27
bubba
29.1k32884
answered Mar 5 '14 at 12:27
bubba
29.1k32884
answered Mar 5 '14 at 12:27
bubba
29.1k32884
29.1k32884
add a comment |Â
add a comment |Â
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You can use complex numbers to calculate the co-ordinates of the new points . Take the init point as $0.5+21i$ and multiply it with $e^itheta$ where $theta = $ the radians by which it is rotated
– AbKDs
Mar 5 '14 at 12:20
In contrast to your other question, this time you have too much information. The radis and angle tell you the arclength.
– bubba
Mar 5 '14 at 12:23