The formulas in part (a) describe a circle of radius `1` centered at the origin.
We can interpret the properties in parts (b) and (c) in the following way: No matter where you start with `theta`, when you increase `theta` by `2 pi` — that is, go once around the circle — you will return to the same function values for cosine (the `x`-coordinate) and sine (the
`y`-coordinate) as when you started.
Part (d) follows from a Cartesian formula for the same circle: `x^2+y^2=1.`
Parts (e) and (f) assert that the `x`- and `y`-coordinates of points on the unit circle always stay between `-1` and `1.`