Unit Circle

The Unit circle is a circle with a center at (0,0) with a radius of 1

The unit circle is used for 0, 90, 180, 270, and 360 degrees or 0, pi/2, pi, 3pi/2, and 2pi in radians

The angle tells you what point to us in the formulas:

sin X = y/r cos X = x/r tan X = y/x

csc X = r/y sec X = r/x cot X = x/y

At 0 degrees, 360 degrees, 0 or 2pi you use the point (1,0)

At 90 degrees or pi/2 you use the point (0,1)

At 180 degrees or pi you use the point (-1,0)

At 270 degrees or 3pi/2 you use the point (0,-1)

Example 1: Find the value of each trig function

a. cos 90 degrees= x/r = o/1 = 0

at 90 degrees x is o and the radius is always 1

b. tan 270 degrees = y/x = -1/0 = undefined

at 270 degrees y is -1 and x is 0 you can never divide by 0 so the answer is undefined

c. sin 360 degrees= y/r = 0/1 = 0

at 360 degrees y is 0 and the radius is always 1

Example 2: Find the value of each trig function

a. tan pi = y/x = 0/-1 = 0

at pi or 180 degrees y is 0 and x is -1

b. cos 3pi/2 = x/r = 0/1 = 0

at 3pi/2 or 270 degrees x is 0 and the radius is always 1

c sin 2pi = y/r = o/1 = 0

at 2pi or 360 degrees y is 0 and the radius is always 1