Reference Angles

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 positive or negative using unit circle methods.

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

Ex 1. Express sin695 degrees in terms of a reference angle

Sin695 – 360 = sin 335 degrees 335 – 360 = sin-25 y/r = neg/1 = negative

Ex 2. Evaluate cos45 degrees =sqrt2/2

Ex 3. Memphis is located at latitude 35 degrees 6 minutes and the city of New Orleans is located at 30 degrees North. How far apart are the two cities?

Theta = 35 degrees 6 minutes = 35.1 degrees

Theta = 5.1 degrees x pi/180 = 17/600pi

S = (3963)(17/600pi) = 352.754mi