Section 4.6 - Graphs of Composite Trigonometric Functions

Essential Question(s): 

Explain the possible outcomes with composing trigonometric functions.

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Follow these three steps to complete this "flip" lesson.

STEP 1: Preparation 
Title your spiral with the heading above and copy the essential question(s).

STEP 2: Vocabulary & Examples 
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your cornell notes.

Combining Trigonometric & Algebraic Functions

• What makes trigonometric functions different? (top pg 405)
• How do you determine periodicity from a graph? (Ex 1 pg 405)
• How do you determine periodicity algebraically? (Ex 2 pg 405)
• How do you use algebraic & graphical methods to analyze a composition? (Ex 3 pg 406)
• What happens to higher odd powers of sine? (mid pg 406)
• How do you analyze nonnegative periodic functions? (Ex 4 pg 406)
• What happens when you add a sinusoid and a linear function? (top pg 407)
• What are the equations when adding a sinusoid to a linear function? (Ex 5 pg 407)

Sums and Differences of Sinusoids

• What does the sum or difference of sinusoids represent and the general form? (mid pg 407 & pg 408)
  
• What are the requirements for a sum or difference to be a sinusoid? (top pg 408)
• How do you determine if a function is a sinusoid or not? (Ex 6 pg 408)
• How do you express a sum of sinusoids as one sinusoid? (Ex 7 pg 408-409)
• What if two sinusoids don't have the same period? (mid pg 409)
• How do you show a function is periodic but not a sinusoid? (Ex 8 pg 409)

Damped Oscillation

• What is damping and a damped oscillation? (pg 409-410)
• How do you identify damped oscillation? (Ex 9 pg 410)
• How can you apply damped oscillation on a spring? (Ex 10 pg 410-411)

STEP 3: Reading
Read the following page(s) and take any extra notes as needed.

• Read pages 405 - 411.
• Make sure to read the paragraphs between the examples.

Graphing Composites Ex #1

Graphing Composites Ex #2

Damped Trig Functions

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