1 / 9

Understanding Angles in Standard Position: Theory and Examples

Learn about angles in standard and non-standard positions, principal and related acute angles, quadrants, and rotation. Solve example problems involving points in the X-Y plane and determining acute and principal angles.

feliper
Download Presentation

Understanding Angles in Standard Position: Theory and Examples

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. q y y x x Day 1: Angles In Standard Position terminal arm initial arm standard position non-standard position terminal arm q q q initial arm 0º

  2. y y Negative angles x rotate clockwise q ex: –120º Positive angles ex: 80º rotate counterclockwise q x

  3. y x Quadrants 90º II I 0º < q < 90º 180º 0º 90º < q < 180º 180º < q < 270º III IV 270º < q < 360º 270º

  4. y y x x Example: P(x, y) Let P(x, y) be a point on the terminal arm of an angle in standard position. q1 Point P can be anywhere in the x-y plane. q1 is in quadrant II. 90º < q1 < 180º 270º < q2 < 360º q2 q2 is in quadrant IV. P(x, y)

  5. y x q3 = 180º P(x, y) q3 q3 lies in the negative x-axis.

  6. y x The principal angle is the angle between 0º and 360º. The related acute angle is the angle formed by the terminal arm of an angle in standard position and the x-axis. q1 b The related acute angle lies between 0º and 90º.

  7. y y y x x x q q b b q = 220º b = 220º – 180º q = 150º = 40º b = 180º – 150º = 30º q = 325º b b = 360º – 325º q = 35º

  8. y x Example 1: The point P(–5, –4) lies on the terminal arm an angle in standard position. a) Sketch the angle. b) Determine the value of the related acute angle. q 5 b 4 P(–5, –4) c) Determine the principal angle q. q = 180º + 39º q = 219º

  9. y x Example 2: The point P(– 6, 7) lies on the terminal arm an angle in standard position. P(–6, 7) a) Sketch the angle. b) Determine the value of the related acute angle. 7 q b 6 c) Determine the principal angle q. q = 180º – 49.4º q = 130.6º

More Related