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GBK Precalculus Jordan Johnson

GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Lesson : Measurement of Rotation Classwork / Homework Return Quizzes Clean-up. Angles. Studied “free-floating” in geometry: To study measurement of rotation, we need a point of reference. (e.g., 12:00 on a clock.)

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GBK Precalculus Jordan Johnson

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  1. GBK PrecalculusJordan Johnson

  2. Today’s agenda • Greetings • Lesson: Measurement of Rotation • Classwork / Homework • Return Quizzes • Clean-up

  3. Angles • Studied “free-floating” in geometry: • To study measurement of rotation, we need a point of reference. • (e.g., 12:00 on a clock.) • Standard position of an angle: initial side terminal side

  4. Standard Position • An angle is in standard positioniff • Its vertex is at the origin, • it has one side (its “initial side”) on the positive horizontal axis, • and it is measured • counterclockwise from the axis if the angle measure is positive, • clockwise if negative.

  5. Coterminal Angles • Now that we have a point of reference, some angles have terminal sides pointing in the same direction: • One is about 55°, the other about 415°.

  6. Coterminal Angles • We need a way of saying these angles are equivalent (in pointing the same direction). • Coterminal angles (in standard position) differ in measure by a multiple of 360°.

  7. Coterminal Angles • Mathematically: • Let α and β be two angles in standard position: • α and β are coterminaliffα = β + 360°∙n, for some integer n. α β

  8. Reference angles • One more definition: • The reference angle of any angle in standard position is the positive acute angle between the horizontal axis and the terminal side. • Comes from triangle trigonometry (a la SOH-CAH-TOA) and is used for our definitions of trig functions. • GeoGebra demo.

  9. Classwork/HW • From Section 2-2: • Q1-Q10 • Problems 1, 5, 9, 19, 21, 25, 27, 29, 30. • Due Friday. • Also for Friday: • Read pp. 66-71.

  10. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and side tables). • See you tomorrow!

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