1 / 19

Understanding Angles: Basic Terms, Measurements, and Operations

Learn the fundamental terminology of angles, degree measures, and how to determine angles in standard position with coterminal angles. Includes complementary and supplementary angles, degree conversions, and coterminal angle calculations.

miltoncooper
Download Presentation

Understanding Angles: Basic Terms, Measurements, and Operations

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. Chapter 1 Trigonometric Functions

  2. Section1.1- Angles Objective: SWBAT learn the basic terminology of angles and their degree measures. In addition students will be able to determine an angle in standard position with coterminal angles.

  3. A B A B A B Basic Terms Two distinct points determine a line called line AB. Line segment AB—a portion of the line between A and B, including points A and B. Ray AB—portion of line AB that starts at A and continues through B, and on past B.

  4. Angle-formed by rotating a ray around its endpoint. The ray in its initial position is called the initial side of the angle. The ray in its location after the rotation is the terminal side of the angle. Vertex-the endpoint of the ray Basic Terms continued…

  5. Positive angle: The rotation of the terminal side of an angle counterclockwise. Negative angle: The rotation of the terminal side is clockwise. Basic Terms continued…

  6. Naming an Angle An angle can be named using its vertex. Ex: angle C An angle also can be named using 3 letters with the vertex in the middle. Ex: angle ACB or angle BCA C . . A . B

  7. Types of Angles • The most common unit for measuring angles is the degree. 360° for a complete rotation of a ray. 1 ° = 1/360 of a rotation. θ is used to name an angle.

  8. Complementary & Supplementary Angles Two positive angles whose sum is 90° are called complementary angles. Two positive angles whose sum is 180° are called supplementary angles.

  9. k+20 k 16 Complementary Angles • Find the measure of each angle. • Since the two angles form a right angle, they are complementary angles. Thus, The two angles have measures of 43 + 20 = 63 and 43  16 = 27

  10. 6x + 7 3x + 2 Supplementary Angles • Find the measure of each angle. • Since the two angles form a straightangle, they are supplementary angles. Thus, These angle measures are 6(19) + 7 = 121 and 3(19) + 2 = 59

  11. Degree, Minutes, SecondsPortions of a degree are measured in minutes and seconds. • One minute is 1/60 of a degree. • One second is 1/60 of a minute. 12° 42’ 38” represents 12 degrees, 42 minutes, 38 seconds.

  12. Perform the calculation. Since 86 = 60 + 26, the sum is written Perform the calculation. Write Calculations

  13. Convert Convert 36.624 ConversionsConverting between decimal degrees and degrees, minutes & seconds.

  14. Warm up • Convert 74° 8’ 14” to decimal degrees. • Convert 34.817° to degrees, minutes, and seconds.

  15. Section1.1- Angles Objective: SWBAT learn the basic terminology of angles and their degree measures. In addition students will be able to determine an angle in standard position with coterminal angles.

  16. Standard Position • An angle is in standard position if its vertex is at the origin and its initial side is along the positive x-axis. • Angles in standard position having their terminal sides along the x-axis or y-axis, such as angles with measures 90, 180, 270, and so on, are called quadrantal angles.

  17. Coterminal Angles • A complete rotation of a ray results in an angle measuring 360. By continuing the rotation, angles of measure larger than 360 can be produced. Such angles are called coterminal angles.

  18. o o - 1115 3(360 ) o = 35 Coterminal Angles • Find the angles of smallest possible positive measure coterminal with each angle. • a) 1115 b) 187 • Add or subtract 360 as may times as needed to obtain an angle with measure greater than 0 but less than 360. • a) b) 187 + 360 = 173

  19. Homework • Worksheet left side

More Related