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GBK Precalculus Jordan Johnson

GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Intro: pp. 95-96, Problems 1-9. Lesson: Characteristics of Sinusoids Classwork: Exploring Sinusoids Homework Clean-up. Quick Check: Answers. Amplitude of y = cos  is 1. Amplitude of y = 5 cos  is 5.

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GBK Precalculus Jordan Johnson

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  1. GBK PrecalculusJordan Johnson

  2. Today’s agenda • Greetings • Intro: pp. 95-96, Problems 1-9. • Lesson: Characteristics of Sinusoids • Classwork: Exploring Sinusoids • Homework • Clean-up

  3. Quick Check: Answers • Amplitude of y = cos is 1. • Amplitude of y = 5 cos is 5. • Period of y = 5 cos is 360°.Same as parent function. • Period of y = cos(3) is 360°/3 = 120°.The 3 is the reciprocal of the dilation factor. • The graph of y = cos( - 60°) is translated horizontally by +60° (rightwards). • The phase displacement is 60°, same as the translation constant. • The graph of y = 6 + cos is translated up by 6.

  4. Answers • The sinusoidal axis is given by the vertical translation. • Given y = 6 + 5 cos 3( - 60°), • Amplitude is 5 • Period is 120° • Phase displacement is 60° • Sinusoidal axis is at y = 6.

  5. Characteristics of Sinusoids • The sinusoidal axis is the line whose y-coordinate is centered in the wave. • The amplitude of a sinusoid is the distance from the sinusoidal axis to the upper value. • i.e., how tall the wave is.

  6. Characteristics of Sinusoids • The period of the wave is the distance from each peak to the next.

  7. Characteristics of Sinusoids • A cycle is a portion of the graph having the length of a period. • i.e., one nonrepeating part. • The phase displacement of a wave is the amount it’s been shifted horizontally.

  8. Review HW • Section 2-6 • R0-R4 • T18-T20

  9. Classwork • P. 90, C2-C3.

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

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