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Unformatted text preview: 4.1 Angles and Their Measures Converting Between Units of Angle Measure Engineers in the ancient world discovered ratios within right triangles, as they learned fundamental Conversion Formulas engineering skills. The secrets and patterns necessary to understanding circles and spheres helped in the development of trigonometry. Our chapter begins the journey into trigonometry with an introduction into angles and their measures. Convert Degrees to Radians multiply degrees by: 180 Convert Radians to Degrees multiple radians by: 180 Angle Characteristics An angle is determined by rotating a ray about its endpoint. EX $4: Convert each angle from radians to degrees or from degrees to radians. The _ Vertex is the endpoint of the ray. ( Rotates ) Terminal side 30 180 = /2109 D. 1350 The Initial side is the starting position. Vertex - 16 TT The Terminal side is the position after 180 2. 20 #1 4 Initial side B. 27 -3200 rotation. (Doesn't) move - LIT Standard Position Angles 15 Angles that are in standard position are placed on a coordinate plane, with the vertex at the origin and the initial side on the Terminal side Practice With Radians positive x-axis. How many radians is each angle of an equilateral triangle? Positive angles are determined by a counterclockwise rotation. 2. The minute hand of a clock travels how many radians in 15 minutes? Negative Vertex Initial side angles are determined by a clockwise rotation. 3 . The minute hand of a clock travels how many radians in 10 minutes? Angle in Standard Position 1 60 . 7805 60 Coterminal Angles 4. The minute hand of a clock travels how many radians in 5 minutes? 30# Two angles in standard position that have the same terminal side are called coterminal angles. We 30 can find an angle that is coterminal to a given angle by adding or subtracting one revolution. So, any 5. What is the measure of O in radians, if * = 45? 5. What is the measure of 0 in radians? given angle has many coterminal angles. For example B = 36 is coterminal to all of the following: 396, 756, -324,-6840 * + 5 X = 180 Beta 360 - 45 = 315 0 6 * = 180 5 x EX #1: Draw 0 = 220 and label 0' as the angle that is coterminal. O could also be 0 = 220' 315 Theta 220' 580 or any full 150 = 220 30 * = 30' + 3 10 revolution 580 ' 140' 2 20" + 340'ny n is an insever O'= - 140 2017 Jean Adams (Flamingo Math Tha) 2017 Jean Adams (Flamingo Math TA) Either will add 340 or sulstreet Positive and negative are different never...
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  • Fall '08
  • ZIEGLER
  • coterminal angles, minute hand of a clock travels

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