Draw a graph of the rose curve. r = 4 cos 2θ, 0 ≤ θ ≤ 2π.

Solution:

The rose curve equation is of the form acos(nθ).

It is given that

r = 4 cos 2θ, 0 ≤ θ ≤ 2π

a= 4 and n = 2

Here n is even. Thus we have 2n petals = 4 petals. The separation between the petals is given as 360º/n = 360º/2 = 180º.

The table below shows the values of cos2θ that we plot between 0 and 2π.

Therefore, the graph of the rose curve is mentioned above.

Draw a graph of the rose curve. r = 4 cos 2θ, 0 ≤ θ ≤ 2π.

Summary:

The graph of the rose curve r = 4 cos 2θ, 0 ≤ θ ≤ 2π is mentioned above. It has 4 petals, separated by 180º.