PPT-Degrees and Radians Initial side – start side of angle

Terminal side end side of angle Standard position An angle whose initial side is on the positive xaxis Positive angles An angle in standard position that rotates counterclockwise Negative angles. Points, Lines, and Angles. 1. Goal . Tell type of angle.. Label angles.. Measure angles. . 2. Review . 3. 4. A? B? C?. Check . a ) ray. b) line segment. c) line . 5. 6. 7. angle. a figure . formed . & Arc Length. Circumference. T. he . distance around a . circle. C = 2. . r . or . d. Ex. : Find the circumference of a circle with a diameter of 12 cm. . C = . d. C = . (12). C = 12. Measur i ng Instruments Tacheometers And Theodolites Angle s & Directions An angle is defined as the difference in direction between two convergent lines . A horizontal angle is formed by the direc by basic rigid motions. A geometric realization of a proof in . H. Wu’s “Teaching Geometry According to the Common Core Standards”. Given two triangles, ABC and A. 0. B. 0. C. 0. .. Assume two pairs of equal corresponding sides with the angle between them equal.. Given circle of radius . r. , a radian is the measure of a central angle subtended by an arc length . s. equal to r. . The radian measure of an arbitrary angle. There are radians in a angle. Why? . Converting Between Degrees and Radians and . Inverse . Trigonometry. Converting Between . Degrees and Radians. When we convert between degrees and radians we multiply by a . . . . The easiest value that is equivalent is . Theodolites. or Transits can Measure:. horizontal angles. vertical angles. distances (stadia). elevations. Components of a Theodolite. Vertical axis. Horizontal axis. Line of sight. Vertical circle. Muon. flux. By Laura Thorsett and . Promita. . Nandy. Introduction. Testing . muon. flux at 8 compass directions and 3 azimuth angles.. Research Questio. n. : At . which angle and direction do . muons. And . Distance. Good angles. Distance and primary viewing angle. Visual indicators at 1B. Plays at 1B. Tag Plays. Views from different angles. Questions. Agenda. WHAT IS A GOOD ANGLE?. Where you keep all four elements in front of you. 9.10.15. Do Now. Define the following:. Acute angle. Straight angle. Right angle. Obtuse angle. Ray. Line. Line segment. How do you prove you are right?. Proving You . A. re Right. We write an explanation of our thinking or thought process. 4 Radians Radians 2/)sln s ln (2/)Sln S ln ( )2ln / sln )2ln / ln A radian: 180 An angle is formed by two rays that have a common endpoint (. vertex). . One ray is the . initial side . and the . other is . the . terminal side. . We typically will draw angles in the coordinate plane with the initial side along . (The Greeks doing trig in fancy dress.). Intro to Trigonometry. For those later influenced by Greek mathematics, trigonometry deals with periodic functions, whose graphs are usually pretty wavy, and whose applications far exceed the polygonal constraints of triangles: periodic motion, sound, and other interesting stuff.. ObjectivesGiven a triangle and three quantities ASA SAS SSS SSA AAS of data about the triangle use the law of sines or the law of cosines to determine the three remaining unknownsDiscussionEvery trian