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Measure of Rotation Lesson for Precalculus Class

Explore measurement of rotation with angles in standard position, coterminal angles, and reference angles. Engaging classwork and homework included. Learn how to find equivalent angles in various orientations.

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Measure of Rotation Lesson for Precalculus Class

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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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