Question

How do you graph `r = 1 + sin(t)`?

Answer 1

See graph and explanation.

Explanation:

The general equation to a cardioid having its dimple at r = 0 is

`r = a(1+cos(t-alpha))`,

a gives the size and `alpha` = inclination of its axis of symmetry to

`t = 0`.

Here, a = 1 and `alpha=pi/2`.

`r (t)` has a period `2pi`.

`sqrt(x^2+y^2)=r = 1+sint>=0` and r in (0, 2), when `t in (0, pi/2)i`.

The graph is symmetrical about `t = pi/2`.

Now, see Socratic graph, depicting all these features.

I have used Cartesian form of the equation.

graph{x^2+y^2-sqrt(x^2+y^2)-y=0 [-5, 5, -2.5, 2.5]}