Does 'using the unit circle' just mean that I use these:

Question

In Quadrant I, theta=beta
In Quadrant II, theta=180-beta
In Quadrant III, theta=180+beta
In Quadrant IV, theta=360-beta

Because the whole lesson we did was about that sort of thing, which is all review from last year, but then at the end we did a quick example saying something about unit circles and every question in my homework is 'using the unit circle'.

Answer 1

The unit circle is the graph of x^2 + y^2 = 1. The radius vector is viewed as the hyp. of a rt triangle and has a magnitude of 1. A vector is assumed to
rotate CCW. So if we start at 0 deg and
calculate the coordinates of the point
where the vector intersects the circle,
we get:

x = 1*cos0 = 1,
y = 1*sin0 = 0,

p(x , y) = (1 , 0).

So coordinates give us the sine and
cosine at any point on the circle.

For a complete graph and more detailed
INFO, GOOGLE,MATH:Unit circle.