Identify, graph, and state the symmetries for the polar equation r=2+2sintheta. which are the critical points in the graph?

Graph = Cardioid

Axis of symmetry = y-axis

Critical points=

Step-by-step explanation:

General equation for this type of cardioid is:

a ± b sinθ

Condition for a cardioid =

Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.

Critical points:

r = 2 + 2 sinθ  ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ  

 ∵derivative of 1 + sinθ = cosθ

For finding critical point the derivative is equal to zero,

2 cosθ = 0    ⇒    cosθ = 0

the value of cosθ is equal to zero at intervals:

So, critical points =

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!