Finding the Polar Area of two circles intersecting each other
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The equations for the two circles are:
$r=18cos{theta}$
$r=3$
$r_f= 9$ and $r_g=3$
I can see that I need to subtract the $r=3$ circle, however im not sure on how to get the boundaries of integration.
I set $18cos{theta} = 9$ and got $pi/3$ and $5pi/3,$ using these boundaries for the equation gives me a wrong number.
It seems like I need help on setting my boundaries. Thanks
calculus area polar-coordinates
edited Dec 1 at 3:28
saulspatz
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
add a comment |
up vote
0
down vote
favorite
The equations for the two circles are:
$r=18cos{theta}$
$r=3$
$r_f= 9$ and $r_g=3$
I can see that I need to subtract the $r=3$ circle, however im not sure on how to get the boundaries of integration.
I set $18cos{theta} = 9$ and got $pi/3$ and $5pi/3,$ using these boundaries for the equation gives me a wrong number.
It seems like I need help on setting my boundaries. Thanks
calculus area polar-coordinates
edited Dec 1 at 3:28
saulspatz
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
1
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
The equations for the two circles are:
$r=18cos{theta}$
$r=3$
$r_f= 9$ and $r_g=3$
I can see that I need to subtract the $r=3$ circle, however im not sure on how to get the boundaries of integration.
I set $18cos{theta} = 9$ and got $pi/3$ and $5pi/3,$ using these boundaries for the equation gives me a wrong number.
It seems like I need help on setting my boundaries. Thanks
calculus area polar-coordinates
edited Dec 1 at 3:28
saulspatz
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
The equations for the two circles are:
$r=18cos{theta}$
$r=3$
$r_f= 9$ and $r_g=3$
I can see that I need to subtract the $r=3$ circle, however im not sure on how to get the boundaries of integration.
I set $18cos{theta} = 9$ and got $pi/3$ and $5pi/3,$ using these boundaries for the equation gives me a wrong number.
It seems like I need help on setting my boundaries. Thanks
calculus area polar-coordinates
calculus area polar-coordinates
edited Dec 1 at 3:28
saulspatz
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
edited Dec 1 at 3:28
saulspatz
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
edited Dec 1 at 3:28
saulspatz
13.3k21327
edited Dec 1 at 3:28
saulspatz
13.3k21327
edited Dec 1 at 3:28
saulspatz
13.3k21327
13.3k21327
asked Dec 1 at 3:23
Daniel2233
133
asked Dec 1 at 3:23
Daniel2233
133
asked Dec 1 at 3:23
Daniel2233
133
133
The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
1
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35
add a comment |
The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
1
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35
The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
1
1
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35
add a comment |
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The equation should be $18cos(theta) = 3$
– Christopher Marley
Dec 1 at 3:25
Oh ya, because you are trying to find the point of intersection correct?
– Daniel2233
Dec 1 at 3:30
Yep! Then $cos(theta) = frac16$ and it gets ugly.
– Christopher Marley
Dec 1 at 3:31
Wow thats even uglier than I had before
– Daniel2233
Dec 1 at 3:33
1
Thanks for the help @ChristopherMarley I ended up getting the right answer, but it was definitely ugly.
– Daniel2233
Dec 1 at 3:35