Question

attach the graph and equations of two limacons one sine and one cosine with the same a and b values your graph may be cardidoids or inner loop dimpled or convex limacons you may use one grid for both graphs or attach separate graphs

Answer 1

The equation of a limacon is

`\begin{gathered} r(\theta)=a+b\cos\theta \\ \text{ or } \\ r(\theta)=a+b\sin\theta \end{gathered}`

I'll use a = 1 and b = 2. This means b > a then the limacon will have an inner loop. Using Geogebra to plot the graphs we get:

As we can see, the blue limacon is the limacon with sin and the green limacon is the limacon with cos