1. 6.1: Angles and their measure January 5, 2008

2. Objectives Learn basic concepts about angles Apply degree measure to problems Apply radian measure to problems Calculate arc length Calculate the area of a sector

3. What is an angle? An angle is formed by rotating a ray around its end point. Important terms: –Initial side: starting position of the ray –Terminal side: the final position of the ray –Positive measure: ray is rotated counterclockwise –Negative measure: ray is rotated clockwise

4. Degree measure One complete rotation is 360°. 90° is a right angle. 180° is a straight angle. Symbols used to denote angles: –Alpha - α –Beta - β –Theta - θ

5. Important angle terms Complementary angles add to be 90°. Supplementary angles add to be 180°. Acute angles 0<θ<90. Obtuse angles 90<θ<180. Coterminal angles: angles with the same terminal side.

6. Radian measure The circumference of a circle is 2π. Therefore, one rotation of ray is 2π radians. To convert from degrees to radians.. Multiply degrees by π/180° To convert from radians to degrees.. Multiply radians by 180°/π 2π = 360° π = 180° π/2 = 90° π/3 = 60° π/4 = 45° π/6 = 30°

7. Try these Degree to radian 120° 150° 200° 320° Radian to degree 2π/5 3π/4 7π/5 6π/5

8. Arc length s= rθ θ must be in radian measure.

9. Try it A circle has a radius of 4. Find the length of an arc intercepted by a central angle of 60°.

10. Try this one A circle has a radius of 12. The arc length of a certain angle is 4. Find the central angle.

11. Area of a sector A= (1/2)r 2 θ θ must be in radian measure.

12. Try it A circle has a radius of 5. Find the area of the sector if the central angle is 75°.

13. Your assignment 1,2 – sketching angles 21-26 – complementary and supplementary 35-38 – find the central angle 43, 44 – converting from degrees to radians 47-52 – find the missing value (arc length) 65-68 – area of a sector