2. Parts of an Angle (the fixed side) (the rotating side) alpha – common angle name Each angle above is said to be in the “standard position” – the vertex is at the origin and the initial side is on the positive x-axis.

3. Example 1 (FYI: The ‘ is read as minutes; the “ is read as seconds)

4. Quadrantal Angle An angle in the standard position in which the terminal side coincides with one of the axes. Examples: Example 2 (Past 360°)

5. Coterminal Angles Two angles in standard position that have the same terminal side. All angles have an infinite number of coterminal angles. Coterminal angles are in the form of: where k is some integer. Example 3 Begin with the generic form to identify all coterminal angles: Choose a positive integer for k to find one positive angle: Choose a negative integer for k to find one negative angle: 45 + 360(1) = 405° 45 + 360(-2) = -675° b. 225° a. 45° 225 + 360(2) = 945° 45 + 360(-1) = -135° 45º 405º (1 loop) 765º (2 loops)

6. Example 4 a. 775°In other words, we need to find the value of alpha in Find the number of rotations (k) by dividing the degree by 360: Determine the leftover degrees: Method 1Method 2: (Partial rotation) k = 2 b. -1297° k = -3 Implies that the coterminal angle should be positive. To convert to a positive angle: Which quadrant does the terminal side of each lie in?Quadrant 2

7. Example 5 Reference angle: an acute angle formed by the terminal side of a given angle and the x-axis. a. 120° Visualize it: 120° Since it’s in Quadrant II: b. -135° -135° Since it’s in Quadrant III: Convert to a positive angle: 360 – 135 = 225 225°

8. HW: Page 280