Unit circles and reference angles.

Unit Circles and Reference Angles :

The unit circle is used for 0, 90, 180, 270, and 360. OR 0, pi/2, pi, 3*pi/2 and 2*pi. The angle tells you which point to use in the 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

Examples:

1. -Cos(-pi) = x/r = -1/1= -1

2. -cos270 degrees= x/r= 0/1= 0 degrees.

Reference angles are like reduced fractions. They must be between 0 and 90 degrees.

Steps:

1. Find the original quadrant and sketch.

2. Determine if the angle is +/- using unit circle methods.

3. Subtract 360 degrees / 180 degrees until absolute value of theta is between 0 and 90 degrees.

Example 1:

Express sin260 degrees in terms of a reference angle.

1. In quadrant 3. = -y/r. = negative

2. 260-180 = 80. (angle is positive.)

sin260 = sin80

Example 2:

Express sin765 degrees in terms of a reference angle.

1. In quadrant 1. = y/r = positive

2. 765-720(360*2)= 45. (angle is positive)

sin 765= sin 45.