1. Advanced Algebra II Advanced Algebra II Notes 10.2 continued Angles and Their Measure

2. Angles: defined as rotation of a ray. Standard position: Vertex at the origin and initial side on positive x- axis. Terminal side: End position of the rotation of the ray. Coterminal angles: angles with the same initial and terminal sides. Positive angle: counterclockwise rotation. Negative angle: clockwise rotation. One rotation = 360° or 2π radians. Quadrant of an angle is determined by the quadrant in which the terminal side lies.

3. Sketch each angle in standard position and state its quadrant: a) 45°b) -90° c) 225°d) 405°

4. Radian: An angle measure in which one full rotation is 2 radians. One radian is the measure of an arc, or the measure of the central angle that intercepts that arc, such that the arc’s length is the same as the circle’s radius.

5. Arc length of a circle: ( angle in radians) Find the length of the arc of a circle of radius 2 meters intercepted by a central angle of.25 radians.

6. Converting degrees and radians: angle in degrees = angle in radians 360° 2 π Convert each angle in degrees to radians: a) 60°b) 150° c) -45°d) 107°

7. Radians to degrees: b radians = Convert each angle in radians to degrees: a) radiansb) radians c) radiansd) 3 radians

8. Area of a sector of a circle: Find the area of the sector of a circle of radius 2 feet formed by an angle of 30°. Round to two decimal places.

9. The Cosmo Clock 21 Ferris wheel at the Cosmo World amusement park in Yokohama, Japan has a 100 m diameter. This giant Ferris wheel makes one complete rotation every 15 minutes. The wheel reaches a maximum height of 112.5 m from the ground. a) Find the speed of a person on this Ferris wheel as it is turning. b) Find the angular speed of this person. is the angular displacement (in radians) s is the arc length or distance (in linear units) is the angular velocity (radians per time) v is the velocity or speed (linear units per time)

10. Assignment: page 578: 1 – 6, 10, 12