Here we can see a circle on top of a coordinate plane (we use x and z here for the horizontal plane of the world), an angle, and two sides of a right triangle, x1 and z1. Using the trigonometry from before we can find the coordinates of any point on a circle by using sine and cosine:
sin(theta) = Opposite over Hypotenuse = z1/radius
cos(theta) = Adjacent over Hypotenuse = x1/radius
After a little multiplication, finding the coordinates of a point is as simple as
x = radius*sin(theta)
z = radius*cos(theta)
We will be using these two equations for our camera model.