Question

What is the smallest interval for theta (0 ≤(theta)≤k) that gives a complete graph of the polar equation r=4cos5(theta)

Answer 1

Usually one cycle of a Cos Function has a period 0 - 2π

now instead of Θ you have 5Θ

so choose values in the interval 0 - 2π and equate it to 5Θ and find the corresponding Θ value

For Example the First Value will be 5Θ = 0 ----> Θ = 0

next 5Θ = 2π ; so Θ = 2π / 5

So one full cycle will be between 0 and 2π/5

Answer 2

how could i use this to discriminate petals on a graph?

Answer 3

do you have the graph?

Answer 4

i entered r=4cos(5theta) into wolfram alpha to get the graph.