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Angles and Their Measure Section 3.1. Objectives Convert between degrees, minutes, and seconds (DMS) and decimal forms for angles. Find the arc length.

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Presentation on theme: "Angles and Their Measure Section 3.1. Objectives Convert between degrees, minutes, and seconds (DMS) and decimal forms for angles. Find the arc length."— Presentation transcript:

1 Angles and Their Measure Section 3.1

2 Objectives Convert between degrees, minutes, and seconds (DMS) and decimal forms for angles. Find the arc length of a circle. Convert from degrees to radians, and from radians to degrees. Find the area of a sector of a circle. Find the linear speed of an object traveling in circular motion.

3 Background Info Ray Vertex Angle –Initial side –Terminal side Counterclockwise/positive rotation Clockwise/negative rotation Standard position

4 Background Info Quadrantal angles/angles that lie in quadrant Measures of rotation: Degrees and Radians

5 Draw the following angles: 45°-90° 225°405°

6 Converting between DMS & Degrees 1 counterclockwise revolution = 360° 1° = 60’ (60 minutes) 1’ = 60” (60 seconds) Make sure calculator is set in degrees mode Example: Convert ° to DMS: Example: Convert 50°6’21” to a decimal in degrees

7 Radians Central angle (θ): angle whose vertex is at the center of a circle Measure of 1 radian: length of radius = arc length Find the arc length (s) of a circle using the following formula: s = rθ Central angle must be in radians in order to use this formula. Example: Page 125 #71

8 Convert from Degrees to Radians and from Radians to Degrees Since one revolution is 360°, and the circumference of a circle equals 2πr, then s = rθ 2πr = rθ θ = 2π radians and 1 revolution = 2π radians Therefore, 180° = π radians

9 Convert from Degrees to Radians and from Radians to Degrees Degrees to radians Multiply by Radians to degrees Multiply by

10 Convert to radians 60° -150° 107°

11 Convert to degrees 3 radians

12 Memorize the table on page 121

13 Pages (11-77 odds) Check answers in the back of the book

14 Find the Area of a Sector of a Circle Example: Find the area of the sector of a circle of radius 2 feet formed by an angle of 30°

15 Find the Linear Speed of an Object Traveling in Circular Motion Linear SpeedAngular Speed

16 Page 126 #97

17 Pages ( odds) Check answers in the back of the book


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