Section 4.3 - Trigonometry Extended: The Circular Functions

Essential Question(s): 

Explain how the trigonometric functions are used to find the others.
Explain the function of the unit circle.

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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.

Trig Functions of any Angle

• What are the initial and terminal sides of an angle? (pg 370)
• What is the measure of an angle? (pg 370)
• What are positive and negative angles? (pg 370)
• Review what standard position is. (pg 370)
• What are coterminal angles? (pg 370)
• How do you know if angles are coterminal? (pg 371 top)
• How do you find coterminal angles? (Ex 1 pg 371)
• How do you evaluate trig functions determined by a point is Q1? (Ex 2 pg 372 & you may want to attempt Exploration 1)
• How do you evaluate trig functions determined by a point in Q2? (Ex 3 pg 372)
• What are the six trig functions for any angle? (pg 373)
• What are quadrantal angles? (pg 375)
• What are the steps to evaluating trig functions of nonquadrantal angles? (pg 374)
• How do you evaluate trig functions determined by a given angle? (Ex 4 & 5 pg 373 - 374)
• How do you evaluate trig functions of quadrantal angles? (Ex 6 p 375)
• Read "Why not use a calculator". (pg 375)
• How can you use one trig ratio to find the others. (Ex 7 pg 376)

Trig Functions of Real Numbers

• Read "Why not degrees?". (Pg 377)
• What is the definition of the unit circle? (Pg 377)
• What is the wrapping function?  (Pg 377)
• What are the trig functions of real numbers? (Pg 378)
• What are circular functions? (Pg 378)

Periodic Functions

• What are periodic functions? (Pg 379)
  
• How can you use periodicity? (Ex 8 pg 379)

The 16-point Unit Circle

• What is the unit circle? (Pg 380)

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

• Read pages 370 - 380.
• Make sure to read the paragraphs between the examples.

The Unit Circle

Interactive Unit Circle

What are Radians?

Unit Circle Graphs

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