Section of a circle
$begingroup$
I need some help with some of my homework, I can't figure it out.
I have a radius on a circle and a height from the circle to the chord.
I found this formula
$$
h=r left(1-cos frac{v}{2} right)
$$
And isolated it to
$$
v = arccos left( frac{h/r -1}{2}right)
$$
Not sure if that's correct. Then I input it in this formula
$$
A=r^2((pi v)/360-(sin v)/2)
$$
I have tried with a radius of 1000 and a height from the circle to the chord of 1000.
But it gives a wrong result.
geometry algebra-precalculus
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
$endgroup$
add a comment |
$begingroup$
I need some help with some of my homework, I can't figure it out.
I have a radius on a circle and a height from the circle to the chord.
I found this formula
$$
h=r left(1-cos frac{v}{2} right)
$$
And isolated it to
$$
v = arccos left( frac{h/r -1}{2}right)
$$
Not sure if that's correct. Then I input it in this formula
$$
A=r^2((pi v)/360-(sin v)/2)
$$
I have tried with a radius of 1000 and a height from the circle to the chord of 1000.
But it gives a wrong result.
geometry algebra-precalculus
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
$endgroup$
$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29
add a comment |
$begingroup$
I need some help with some of my homework, I can't figure it out.
I have a radius on a circle and a height from the circle to the chord.
I found this formula
$$
h=r left(1-cos frac{v}{2} right)
$$
And isolated it to
$$
v = arccos left( frac{h/r -1}{2}right)
$$
Not sure if that's correct. Then I input it in this formula
$$
A=r^2((pi v)/360-(sin v)/2)
$$
I have tried with a radius of 1000 and a height from the circle to the chord of 1000.
But it gives a wrong result.
geometry algebra-precalculus
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
$endgroup$
I need some help with some of my homework, I can't figure it out.
I have a radius on a circle and a height from the circle to the chord.
I found this formula
$$
h=r left(1-cos frac{v}{2} right)
$$
And isolated it to
$$
v = arccos left( frac{h/r -1}{2}right)
$$
Not sure if that's correct. Then I input it in this formula
$$
A=r^2((pi v)/360-(sin v)/2)
$$
I have tried with a radius of 1000 and a height from the circle to the chord of 1000.
But it gives a wrong result.
geometry algebra-precalculus
geometry algebra-precalculus
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
edited Jun 28 '12 at 19:52
Arturo Magidin
264k34587915
264k34587915
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
asked Jun 28 '12 at 11:35
NikolajSvendsenNikolajSvendsen
32
32
$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29
add a comment |
$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29
$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
The problem is that your solution is incorrect. You have the 2 factor in the wrong place. the correct solution is:
v=2arccos((1-h/r)
answered Jun 28 '12 at 12:45
BarryBarry
25612
$endgroup$
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
add a comment |
$begingroup$
Yep, that is correct:
$v=2arccos(1-frac{h}{r})$
And this is how we get it:
$cos(frac{v}{2}) = frac{r-h}{r}$
$cos(frac{v}{2}) = 1-frac{h}{r}$
$frac{v}{2} = arccos(1-frac{h}{r})$
$v=2arccos(1-frac{h}{r})$
See this homework help resource for more.
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The problem is that your solution is incorrect. You have the 2 factor in the wrong place. the correct solution is:
v=2arccos((1-h/r)
answered Jun 28 '12 at 12:45
BarryBarry
25612
$endgroup$
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
add a comment |
$begingroup$
The problem is that your solution is incorrect. You have the 2 factor in the wrong place. the correct solution is:
v=2arccos((1-h/r)
answered Jun 28 '12 at 12:45
BarryBarry
25612
$endgroup$
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
add a comment |
$begingroup$
The problem is that your solution is incorrect. You have the 2 factor in the wrong place. the correct solution is:
v=2arccos((1-h/r)
answered Jun 28 '12 at 12:45
BarryBarry
25612
$endgroup$
The problem is that your solution is incorrect. You have the 2 factor in the wrong place. the correct solution is:
v=2arccos((1-h/r)
answered Jun 28 '12 at 12:45
BarryBarry
25612
answered Jun 28 '12 at 12:45
BarryBarry
25612
answered Jun 28 '12 at 12:45
BarryBarry
25612
answered Jun 28 '12 at 12:45
BarryBarry
25612
25612
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
add a comment |
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
Thanks that works. But can you explain me how v, can be 180 degress. Isn't it a triangle like on this image matb1htx.systime.dk/fileadmin/indhold/ISBNXXXXXXXXXXXXX/…
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:59
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
$begingroup$
In your example, the height to the chord is equal to the radius. Therefore the chord becomes a diameter and the angle subtended by a diameter is 180 degrees.
$endgroup$
– Barry
Jun 28 '12 at 13:12
add a comment |
$begingroup$
Yep, that is correct:
$v=2arccos(1-frac{h}{r})$
And this is how we get it:
$cos(frac{v}{2}) = frac{r-h}{r}$
$cos(frac{v}{2}) = 1-frac{h}{r}$
$frac{v}{2} = arccos(1-frac{h}{r})$
$v=2arccos(1-frac{h}{r})$
See this homework help resource for more.
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
$endgroup$
add a comment |
$begingroup$
Yep, that is correct:
$v=2arccos(1-frac{h}{r})$
And this is how we get it:
$cos(frac{v}{2}) = frac{r-h}{r}$
$cos(frac{v}{2}) = 1-frac{h}{r}$
$frac{v}{2} = arccos(1-frac{h}{r})$
$v=2arccos(1-frac{h}{r})$
See this homework help resource for more.
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
$endgroup$
add a comment |
$begingroup$
Yep, that is correct:
$v=2arccos(1-frac{h}{r})$
And this is how we get it:
$cos(frac{v}{2}) = frac{r-h}{r}$
$cos(frac{v}{2}) = 1-frac{h}{r}$
$frac{v}{2} = arccos(1-frac{h}{r})$
$v=2arccos(1-frac{h}{r})$
See this homework help resource for more.
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
$endgroup$
Yep, that is correct:
$v=2arccos(1-frac{h}{r})$
And this is how we get it:
$cos(frac{v}{2}) = frac{r-h}{r}$
$cos(frac{v}{2}) = 1-frac{h}{r}$
$frac{v}{2} = arccos(1-frac{h}{r})$
$v=2arccos(1-frac{h}{r})$
See this homework help resource for more.
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
edited Jun 29 '12 at 12:49
rschwieb
107k12102251
107k12102251
answered Jun 28 '12 at 19:51
KliKli
1
answered Jun 28 '12 at 19:51
KliKli
1
answered Jun 28 '12 at 19:51
KliKli
1
1
add a comment |
add a comment |
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$begingroup$
What is given, what do you search for? So given: radius r, and distance to (some) chord h. What is $v$?
$endgroup$
– Simon Markett
Jun 28 '12 at 11:57
$begingroup$
I want to find the areal, of the circle section. R=1000, Distinace to chord=1000. Then i calculate v in the first formula.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:07
$begingroup$
When the radius and distance to the chord is exactly the same, it should be the half of the circle. But it gives a wrong result, i am not sure whetever i mixup radians and degress, or i isolated it wrong.
$endgroup$
– NikolajSvendsen
Jun 28 '12 at 12:29