6.1

1. 6.1 Angles and Radian Measure

2. (0,1) x = 1 Radian  0  (1,0) (-1,0) 2 (1,0) (0,-1) 57.3 1 Radian = x x = 1 Radian  180   1 Radian x = 57.3 Radius 1 Radian is defined as the angle that intersects an arc having the same length as the radius of that circle. It measures approximately 57.3.

3. (0,1) x = 1 Radian  0  (1,0) (-1,0) 2 (1,0) (0,-1) 57.3 1 Radian = x x = 1 Radian  180   1 Radian x = 57.3 Radius 1 Radian is defined as the angle that intersects an arc having the same length as the radius of that circle. It measures approximately 57.3.

4. 8.1 Radian Measure An angle with its vertex at the center of a circle that intercepts an arc on the circle equal in length to the radius of the circle has a measure of 1 radian. • The radian is a real number, where the degree is a unit of measurement. • The circumferenceof a circle, given by C = 2 r, where r is the radius of the circle, shows that an angle of 360º has measure 2 radians.

5. 8.1 Converting Between Degrees and Radians • Multiply a radian measure by 180º/ and simplify to convert to degrees. For example, • Multiply a degree measure by  /180º and simplify to convert to radians. For example,

6. Convert • 1. 330 degrees to radians… • 2. to degrees…

7. You should memorize this. This is a great reference because you can figure out the trig functions of all these angles quickly.

8. Arc Length The length of any circular arc, s, is equal to the product of the measure of the radius of the circle, r, and the radian measure of the central angle, , that it subtends. Or s = r. Find the length of an arc that subtends a central angle of 42 in a circle of radius 8cm. First, convert degrees to radians.

9. Area of a Circular Sector

10. Ex: • Find the area of a sector if the central angle measure 5pi/6 radians and the radius of the circle is 16cm.