[Maxima] cardioid

Sun Mar 30 12:40:08 CDT 2008

```Hi

> On Sunday 30 March 2008 19:34, Adam Majewski wrote:
>
>>> You're converting expression to polar form incorrectly.
>> Yes but where is my error ?
>
>>> You should get r=r(theta) from {r=r(t),theta=theta(t)} by excluding
>>> parameter t (which is not an argument).
I have r=r(theta) :

(%i7) e1:exp(theta*%i)/2-exp(2*theta*%i)/4;
(%o7) %e^(%i*theta)/2-%e^(2*%i*theta)/4
(%i8) r:abs(e1);
sqrt((sin(theta)/2-sin(2*theta)/4)^2+(cos(theta)/2-cos(2*theta)/4)^2)

>> I have changed name "t" to "theta" ( I didn't know that it has meaning)
>> but it gives the same curve.
>
> No, it hasn't special meaning for Maxima plotter. t is just not an polar angle
> here. As I wrote, standard way is to exclude t and get r=r(theta) from
> {r=r(t),theta=theta(t)}, but in this case you should start from known polar
> equation.
>
>> Anyway, it's better to start from known polar equation of cardioid
>>
>>>   r = a (1-cos(theta)).
>>>
>>> So, parametric equations are ...
>> Yes parametric form works well.
>> Can it be done in polar form ?
>> (:-))
>
> As I wrote, a = 1/2.

So you mean:

r:  (1-cos(theta))/2;