The Unit Circle

The unit circle is use for 0, 90, 180, 270, 360(in degrees) and 0, pi/2, pi, 3pi/2, and 2pi(in radians).

The angle tells you which point to use in the formulas.

Formulas: sin theta = y/r cos theta = x/r tan theta = y/x csc theta = r/y sec theta = r/x cot theta = x/y (r always = 1)

Each value corresponds with a point.

0 degrees, 360 degrees, 0, 2pi – (1,0)

90 degrees, pi/2 – (0,1)

180 degrees, pi – (-1,0)

270 degrees, 3pi/2 – (0,-1)

Ex. 1 Find the value of:

a. sin 90 degrees = y/r = 1/1 = 1

b. cos(-pi) = x/r = -1/1 = -1

c. tan(-pi/2) = y/x = -1/0 = undefined

d. cos 270 degrees = x/r = 0/1 = 0

Ex. 2 State whether the following are positive or negative:

a. sin 165 degrees = y/r = 1/1 = positive

b. sin 265 degrees = y/r = -1/1 = negative

c. cos 210 degrees = x/r = -1/1 = negative