1. An angle whose vertex is at the center of the circle is called a central angle. The radian measure of any central angle of a circle is the length of the intercepted arc divided by the circle’s radius. One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

2. Convert Degrees to Radians and Radians to Degrees. Methods for converting. Convert each angle in degrees to radians: a. 60° b. 270° c. –300° Reduce by 60 and cancel the degree symbols. Reduce by 90 and cancel the degree symbols. Reduce by 60 and cancel the degree symbols. 1. Multiply a degree measure by radian and simplify to convert to radians. 2. Multiply a radian measure by and simplify to convert to degrees.

3. Convert each angle in radians to degrees: a. b. c. Reduce by 4 and cancel the pi symbols. Reduce by 3, cancel the pi symbols, and multiply 60(-4). Type this into your calculator.

4. In the figure below, each angle is in standard position, so that the initial side lies along the positive x-axis. Positive Rotation (Counter-clockwise) Find each function value.

5. The length s of the arc intercepted on a circle of radius r by a central angle radians is given by the formula where is in radians. The area, SA, of the sector of a circle of radius r and central angle is given by the formula where is in radians. A circle has radius 18 cm. Find the arc and sector area intercepted by a central angle having each of the following measures. Convert to radians!

6. The arc length has to be the same distance for both gears, however that doesn’t mean that the central angles will be the same!

7. 3.14 1.57 4.71

8. Where is x = 0. Where is y = 0. This expression gives us a list of odd factors. Change MODE to RADIANS!

9. Quadrant 4 [ 4.71, 6.28 ] Quadrant 3 Change MODE to DEGREES! Reference angle is in Quadrant 1, Now the radians is in our interval.

10. Linear Speed = distance traveled per unit of time. Angular speed = amount of rotation per unit of time. Linear speed in terms of Angular Speed. A point in motion on a circle of radius r through an angle of radians in time t is linear speed(v).

11. Linear Speed of an Earth Satellite. An earth satellite orbits the earth 1200 km high makes one complete revolution every 90 minutes. What is its linear speed? Radius of the earth is 6400 km. To use the formula we need to find the radius and omega. 1200km 6400km

12. Angular Speed and Linear Speed. The blades of a wind turbine are 116 feet long. The propeller rotates at 15 revolutions per minute. What is the angular speed? What is the linear speed? Angular speed radians per minute. The linear speed is given, feet per min.

13. Angular Speed of a winch. A crab trap is hoisted at a rate of 2 ft/sec as the cable is wound around a winch 1.8 yd in diameter. What is the angular speed? We need to solve for omega, so here are the two formulas with omega. The linear speed is given, and the radius needs to be determined in feet. We don’t know the rotation, so the formula with theta is out and we were given 2 ft/sec which is linear speed. Solve the linear speed formula for omega.

14. Angular of rotation. A car traveling at 70 mph has tires that measure 28.56 inches. What is the angular rotation through which the tire rotates in 10 seconds? We need the angular rotation formula and solve for. We are given the rate 70 mph which is linear speed. Use and solve omega,. Convert to feet per seconds. Convert to feet.