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

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.

(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