Circular Trig

angle - formed by rotating a ray around its endpoint initial side - the ray in its starting position terminal side - the ray’s location after rotating terminal side angle initial side

A rotation upward creates a positive angle. A rotation downward creates a negative angle.

Example 1: Draw each angle.

We don’t have to stop at 360! Draw 497. 137 more 137 and 497 are coterminal angles because they stop in the same place. 360 497 altogether!

Example 2: For the angles below, find the smallest positive coterminal angle. (Add or subtract 360 as may times as needed to obtain an angle with measure greater than 0 but less than 360.) a) 1115 b) 187

Classifying Angles Angles are often classified according to the QUADRANT in which their terminal sides lie. Example: 50º is a ____ quadrant angle. 208º is a ____ quadrant angle. II I -75º is a _____ quadrant angle. III IV

Standard position angles that have their terminal side on one of the axes are called QUADRANTAL ANGLES. For example, 0º, 90º, 180º, 270º, 360º, … are quadrantal angles.

What’s a radian? Radian measure is just a different way of talking about the circle. Just as we can measure a football field in yards or feet--we can measure a circle in degrees or in radians!

Think about what the word radian sounds like… it sounds like “radius,” right? It turns out that a radian has a close relationship to the radius of a circle.

Example 3: Convert each degree measure to radians. (a) 30° (b) 120° (c)  60° (d) 270° (e) 104 °

Example 3: Convert each radian measure to degrees.

A Sense of Angle Sizes See if you can guess the size of these angles first in degrees and then in radians. You will be working so much with these angles, you should know them in both degrees and radians.