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.

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

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

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: (1) = 405° (-2) = -675° b. 225° a. 45° (2) = 945° (-1) = -135° 45º 405º (1 loop) 765º (2 loops)

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 ° 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

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 = °

HW: Page 280