We have to identify the polar form equation in the graph.
The function has a value of r that varies between 0 and 4.
We can then discard Option C, as the function does not have a constant value.
We can see that the maximum value that the function has is r = 4.
With this we can discard Option B, as 4 + cos(θ) has a maximum value of 5.
We now have two similar functions, 4sin(4θ) and 4cos(4θ).
We can now check with the particular values of each function.
For example, when θ = 0, the sine has a value of 0 and the cosine has a value of 1.
In this case, for θ = 0, the function has its maximum value (r = 4), so the trigonometric function has to have its maximum value, which is 1.
This tells us that the trigonometric function is a cosine (NOTE: when there is no phase shift, like this case).
Then, the function is 4cos(4θ).
Answer: 4cos(4θ) [Option D]
