Polar Coordinates and integration

[newageslackr]

I have a basic understanding of the polar coordinate system. I have some questions that would help me with my hw though.

 

(1) how do I take an equation like 3cos(5 theta) and figure out how big an interval is for one loop. I know that there are 5 loops, i just don't know how to get the interval.

 

(2)i know that when integrating to get area im going to take .5( integral from angle a to angle b of r^2 dtheta)

 

i also know that if im finding the area between two curves i take the difference of r1^2 and r2^2 depending on whic yields a greater value, would i break the intervals up for when one function was greater then the other.

 

any help is appreciated

[s pepperchin]

I have a basic understanding of the polar coordinate system. I have some questions that would help me with my hw though.

 

(1) how do I take an equation like 3cos(5 theta) and figure out how big an interval is for one loop. I know that there are 5 loops' date=' i just don't know how to get the interval.

 

(2)i know that when integrating to get area im going to take .5( integral from angle a to angle b of r^2 dtheta)

 

i also know that if im finding the area between two curves i take the difference of r1^2 and r2^2 depending on whic yields a greater value, would i break the intervals up for when one function was greater then the other.

 

any help is appreciated[/quote']

 

For the first question how do you get that there are 5 loops?

 

for the second you would just take the integral of the outer radius and subtract the area for the inner radius and that would give you your answer.

[nicobudini]

(1) how do I take an equation like 3cos(5 theta) and figure out how big an interval is for one loop. I know that there are 5 loops' date=' i just don't know how to get the interval.

[/quote']

 

First, the equation is r(theta)=3*cos(5*theta), isn't it?

 

The polar plot of this equation gives a 5 loops flower-like graph. So you are right, there are 5 loops or petals. Each of the petals converges in r=0.

To get the interval of one loop you have to figure out the first value of theta for which r(theta)=0 and then multiply it by 2.

 

For example, the maximum value for r is r(0)=3

Now, r(theta)=0 for theta=Pi/10, cos(theta) is an even function so r(-Pi/10)=0 too ==> the theta interval for one loop or petal is 2*Pi/10=Pi/5.

 

Hope this helps...

 

Greetings

Nicolas