Unit Circle

The unit circle is a circle with radius 1. It is used to find 0°, 90° (π/2), 180° (π), 270° (3π/2), 360° (2π), and all coterminal angles of them.

Whatever angle is given is the point you will use in the formulas.

sinΘ = y/r cosΘ = x/r tanΘ = y/x
cscΘ = r/y secΘ = r/x cotΘ = x/y

An easy way to remember them is to learn the top three, and then the bottom three are their inverses. If you get csc and sec confused, just remember that sin cannot go with sec because they both start with s, and cos and csc cannot go together because they both start with c.

Ex. 1
sin(90°)
1. sin is y/r
2. The point at 90° is (0,1)
3. The radius is 1, so plugging into y/r, you get 1/1, which is 1.

Ex. 2
tan(-π/2)
1. tan is y/x
2. Convert the radians to a degree. The radian π/2 is 90°. Because it's negative, you would go 90° counter-clockwise, putting you at 270°.
3. The point at 270° is (0,-1)
4. Plugging in, you get -1/0, which is undefined.

If the question just asks to state whether it is positive or negative,
1. Determine which quadrant the angle given is.
I. (+,+) II. (-,+) III. (-,-) IV. (+,-)
2. Find the formula for the trig function given. (Ex. Sin is y/r)
3. Identify if the answer is negative or positve.

Ex.1
cos(210°)
1. The angle is in the third quadrant, where both the y's and x's are negative.
2. cos is x/r
3. It is negative, because you get a -#/1.