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Unformatted text preview: Section 4.1- Definitions 1. Basic Definitions and Facts Ray: part of a line made up of an endpoint and all the points on one side of the endpoint. Angle: formed by rotating a ray about the endpoint. . 9 Initial Side: rays original position Terminal Side: rays position after a rotation. 1'2"“ “-gl Vertex of the angle: endpoint - ' 9 P03 1+1 v e Anc‘l e Positive Angle: rotation is counter-clockwise max Negative Angle: rotation is clockwise Central Angle: An angle whose vertex is at the center of a circle. warmer Angie RightAngIe: Has a measure of 90 degrees. Acute Angle: Has a measure between 0 and 90 degrees. Obtuse Angle: Has a measure between 90 and 180 degrees. StraightAngle: Has a measure of 180 degrees. 1 degree: the measurement of the angle that is the result of going 1/3 60th revolutions counterclockwise around the vertex. Tahe radian me sure 5 of acentral anglethat nterce ts anarc o (velrcle of radifi risgiven by L 1 . ., A? L 11. The Rectangular Coordinate System and the Measuring Angles I! "\ Recall the Rectangular Coordinate System: ._< *\ (1* ‘ *3 , The Rectangular Coordinate System can be though fas 4 Quadrants, labeled counterclockwise as I, II, III, and IV o °lO An angle in a rectangular coordinate system is in standard position if its vertex is at the origin and its initial side lies on the positive x-axis. a 1n!*\OL\ Example 1 g $0 g Slé? Draw each of the follow angles in standard position . ° up a] 60 degrees \53 ° b -240 de rees ’ To convert from Degrees, Minutes, Seconds to Decimal Degrees, simply use the "2ml +" or "DMS>DD” button on the TI-30XA. To convert from Decimal Degrees to Degrees, Minutes, Seconds, simply use the "2nd =” or "DD>DMS” button on the TI-30XA. Example Two a] Convert 24 degrees, 8 minutes, and 15 seconds to decimal degree notation. Round the answer to two decimal places. 2:13:56 24.035 —7 20:.l315 :— b] Convert 67.526 degrees into degrees, minutes and seconds. (.1521; —-+ tn" 3v 3’5“ c. 111. Converting Between Degrees and Radians 6'1. 3“ 3H “ The key to converting back and forth between degrees and radians is knowing that \so° = 'vr radian: or \eo Seam =‘W «no a F Deg ees to Radians: Podxons= ,_ 9- cas. .t Radians to Degrees: a) Convert 30 degrees to radians ‘ m0 . 'T“ -=. T,“ \80’ o :1 b) Convert -225 degrees to radians 0) 1r “115‘1="§E c] Convert _a to degrees \80° “l 7i0°=l¢0° 0".- 3% IV. Compliments and Supplements ‘19 Two positive angles are complements 'fi the sum of their measures is 90 degrees. Two positive angles are supplements if the sum of their measures is 180 degrees. Note: Every Angle_ e such that9_ < 180 degrees will have a supplement. Not all angles will have a compliment. Example Four: Find the compliment and supplement of each angle: 0. qo°~=13°= 11° a] 73degrees S1 1%b°- .13. g ‘01.: b) 110 degrees NO Cm?\‘1men-1- . 5: 180°~11o° = no“ V.ArcLength Def. 5 ”5‘9 s=1erg+h 01mm 1' = rodws 9: measure a? cam-rad awe Example Five m (Gd-10h ‘ circle has a radius of 18 inches. ind the 4 intercepted by a tr angle with a measure of 210 degrees. 3 _ r . e V = \3 Inches 3 '-' ‘3 . Sufi-1 = w * 1%“ o __ V30 (9 : \ZCD'“ .. 2““ VI. Area ofa Sector (9 = (a 5 .q‘j “ A §Q_C*°(of a circle is a region bounded by the two sides of a central angle and the intercepted arc. The area, A, of a sector of acircle with radius r formed by a central angle with radian measure Qis A— ' \ S “e. 2 Example Six How many square inches of pizza have you eaten (rounded to a whole number) W if you eat a slice of an 18 inch diameter pizza whose edges fine a 30 degree angle? “em mum“ 2:81p- ‘11" . #.wfl_,-.7f-. . 1 L.‘ «,1: .11 ...
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