1. Angles and Radian Measure Section 4.1

2. Objectives Estimate the radian measure of an angle shown in a picture. Find a point on the unit circle given one coordinate and the quadrant in which the point lies. Determine the coordinates of a point on the unit circle given a point on the unit circle. Find coterminal angles. Convert angle measures between radians and degrees. Determine the linear speed of an object traveling in a circular motion. Determine the arc length on a given circle.

3. Vocabulary unit circle radian measure of an angle (radians) degrees vertex of an angle terminal side of an angle initial side of an angle linear speed (length per unit of time) length of a circular arc angular speed (radians per unit of time)

4. Unit Circle

5. Consider the picture below. The angle θ is an integer when measured in radians. Give the measure of the angle.

6. Coterminal Angles: Angles are coterminal if they are in standard position and have the same terminal side. Find an angle between 0 and 2π that is coterminal to the angle

7. Conversion between degrees and radian Length of a circular arc Linear speed Angular speed Formulas

8. Find the degree measure of an angle with radian measure

9. Find the radian measure of an angle with degree measure

10. Find the length of the arc on a circle of radius r = 6 inches intercepted by a central angle θ = 135 degrees

11. A Ferris wheel has a radius of 30 feet and is rotating at 3.5 revolutions per minute. Find the linear speed, in feet per minute, of a seat on the Ferris wheel.