Graphing Paramenters for Polar Equations

[RallyToMe]

I am trying to graph just part of a polar equation. For example, the equation r = 2 cos (3θ) when graphed will give you a three-petaled flower shape. I need to find the area of just one of the petals, so I need to know what the bounds of each is. What is the best way to go about doing this?

Thanks,

[Maké]

You can write the equation and plot polar, of three petaled flower and ...

The equation what you indicated, is for a circle.

Now, can you indicate what petal you needed find the shape area ?. 

See, the Lesson 16, page 32/33, for area, from ... 

HP 50g Tutorial - Thiel College

[RallyToMe]

Indeed, I meant 2 cos (3θ). I need to find the area of any one of the petals, but may also need to find the areas of cardiods and other shapes.

[Tim_Wessman]

Been a while since I've done this, but don't you just need to do:

int(1/2*(<your_function>)^2, <var> , <start>, <finish> ) 

example:

∫((1/2)*(2*cos(3*θ))^2,θ,0,π/3)  => ~1.047...

For any of them? If it converges, you should be good I think.

[RallyToMe]

Hello,

The problem is, I am not given the start and end points, otherwise that would be exactly what I would do.

[Maké]

You needed calculate, the area, of one petal, of ... https://math.stackexchange.com/questions/328744/find-the-area-of-the-roses-petal

[BartdB]

Hi,

When you have the three petal shape in the plot window select  TRACE (F3) then (X,Y) (F2), you should now see θ and Y co-ordinates at the bottom of the screen.

Use the left & right buttons to step round the graph and find the co-ordinates of the required points.

To export co-ordinate values to the stack:

press a function key to see the menu again

select EDIT and press NXT twice then select X,Y->

Select PICT and  (X,Y) to go back to finding co-ordinates (TRACE should still be active)

When you exit graph mode the values will be on the stack.

Then use the θ values in the method in Tim Wessman's reply to find the area.

[Maké]

Hi!, @RallyToMe:

See, the Lesson 16, page 32/33, for area, from ... 

HP 50g Tutorial - Thiel College

[BartdB]

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@Maké wrote:

@hi!, @RallyToMe:

See, the Lesson 16, page 32/33, for area, from ... 

HP 50g Tutorial - Thiel College

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However please note that  FCN  is not available in Polar plots, but it is indeed very useful for Function plots.

[Jan_D]

In addition to which has been said already:

A petal begins when r=0 and ends when r=0 again.

So you have to integrate from one zero of r(θ) to another zero of r(θ).

The zeros of cos(3θ) are: 3θ=π/2+n.π,

so θ= π/6+ π/3.n

So you could integrate from π/6 to π/6+ π/3

This is the corresponding petal for this range and “auto” pressed in the menu of Plot Window