Answer: Option C.
Explanation:
We have functions of r(θ)
In our graph, we can see that the minimum value of r is when θ = 0°, and the maximum value is when θ = 180°.
We also know that the graph is in the square (-5, 5)x(-5, 5) and you can see that the maximum radius is almost less than 5.
Then let's analyze the options:
A) r = 3 - 2*cos(θ)
the maximum is at the right angle, but the maximum is:
r = 3 -2*(-1) = 5, so this maximum value is bigger than the one in the graph.
B) r = 3 - sin(θ)
For the sin functions, the maximum and minimum do not correspond with the values i write earlier, so we can discard this option.
C) r = 3 - cos(θ)
The maximum is: r = 3 - (-1) = 4, so this may be the correct answer.
the minimum is r = 3 - 1 = 2,
this is a possible equation for our circle.
D) r = 2 - 2*cos(θ)
Here, when θ = 0, we have: r = 2 - 2*1 = 0, but in the graph we can see that the radius is not 0 when θ = 0, so we can discard this option.
So the only option that makes sense is option C.