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:
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.
Background Info Ray Vertex Angle –Initial side –Terminal side Counterclockwise/positive rotation Clockwise/negative rotation Standard position
Background Info Quadrantal angles/angles that lie in quadrant Measures of rotation: Degrees and Radians
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 21.256° to DMS: Example: Convert 50°6’21” to a decimal in degrees
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
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
Convert from Degrees to Radians and from Radians to Degrees Degrees to radians Multiply by Radians to degrees Multiply by