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GBK Precalculus Jordan Johnson

GBK Precalculus Jordan Johnson. Today’s agenda. Greetings Review / Submit HW: From Section 5-3: Exercises 14, 17-33 odd, 36. Bonus : 41. From Section 5-4: Reading Analysis questions Exercises Q1-Q10 Exercises 1, 3, 5. NaQ on Harmonic Analysis

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GBK Precalculus Jordan Johnson

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  1. GBK PrecalculusJordan Johnson

  2. Today’s agenda • Greetings • Review / Submit HW: • From Section 5-3: • Exercises 14, 17-33 odd, 36. • Bonus: 41. • From Section 5-4: • Reading Analysis questions • Exercises Q1-Q10 • Exercises 1, 3, 5. • NaQ on Harmonic Analysis • Lesson: Sums, Products, and “greatly different periods” • Classwork / Homework • Clean-up

  3. On sinusoids of different periods • The text has addressed how to graph the product of sinusoids of “greatly different periods”.

  4. Sums and Products • Write an equation for y as a product of two sinusoids. Confirm with your grapher that the equation is correct. • What are the periods of the two sinusoids?

  5. Sums and Products • On the same screen, plot the graph of: • y = cos 10 + cos 8 • What do you notice?

  6. Sums and Products • What are the periods of the two sinusoids in y = cos 10 + cos 8? • How are the arguments to cosine in this equation related to those of the one you found earlier?

  7. Sums and Products: Problem • Prove algebraically that the two equations are equivalent.

  8. Formulas • We know: • sin(A + B) = sin A cos B + cos A sin B • sin(A – B) = sin A cos B – cos A sin B • By addition/subtraction, we can derive: • sin(A + B) + sin(A – B) = 2 sin A cos B • sin(A + B) – sin(A – B) = 2 cos A sin B

  9. Formulas • Likewise for cosine: • cos(A + B) = cos A cos B – sin A sin B • cos(A – B) = cos A cos B + sin A sin B • By addition/subtraction: • cos(A + B) + cos(A – B) = 2 cos A cos B • cos(A + B) – cos(A – B) = -2 sin A sin B • cos(A – B) – cos(A + B) = 2 sin A sin B

  10. Classwork / HW • From Section 5-4: • Exercises 7, 9, 11. • Bonus: Exercise 12. • Musical Harmony problems.

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

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