1. Chapter 13: Trigonometric and Circular Functions Section 13-2: Measurement of Arcs and Rotations

2. Objectives Given the angle measure, q, or the arc length, x, sketch the position of the point P on the unit circle.

3. Standard Position A directed angle or arc beginning at the positive u-axis and measured counterclockwise is said to be in standard position. Thus, if q or x is negative, the angle or arc would be measured in the clockwise direction.

4. Examples Graph the following angles: 57º 133º -251º 560º

5. Coterminal Angles or arcs in standard position are said to be coterminal if they terminate (end) at the same place. Coterminal arcs or angles differ by an integral number of revolutions. Example: 60º and 420º are a pair of coterminal angles.

6. Reference Angle In order to draw an angle or arc in standard position, it helps to find the measure of the acute angle between the terminal side and the u-axis. This angle is called the reference angle

7. Finding the Reference Angle We have formulas for finding the reference angle, but it is often easier to figure out the reference angle by drawing a picture. Reference Angle Formulas: If q terminates in Quadrant I: q ref = q If q terminates in Quadrant II: q ref = 180º – q If q terminates in Quadrant I: q ref = q - 180º If q terminates in Quadrant IV: q ref = 360º – q

8. Example: Find the reference angles for the following angles: 156º 214º 336º 4897º

9. Radians Sketch an arc of a unit circle measured in standard position on the unit circle when: *Note: First, find the measure of the corresponding central angle for the given radian measure. First, find the measure of the corresponding central angle for the given radian measure.

10. HOMEWORK: p. 717 #1-23 odd