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Trigonometry/Pre-calculus

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Trigonometry/Pre-calculus

January 10, 2011

Draw a 30-60-90 triangle and list the non-decimal values for the following trigonometric functions (i.e., leave radicals as radicals, so you can’t use your calculator!):

- sin 45°
- cos 60°
- tan 30°
- csc 60°

- Outline of rest of quarter 2
- January 10 to February 11, 2011
- 24 class days
- 5 weeks
- Martin Luther King, Jr. Holiday, January 17 (next Monday)

- Today: review of functions
- Chapter 3: next 6 days (quiz next week)(quiz 1/21)
- Chapter 4: about 2 weeks (quiz 2/1)
- Chapter 5: a bit less than 2 weeks (quiz 2/10)
- Long-term assignment: MANDATORY
- Extra-credit for those who got it in on December 7, 2010
- I will call your parents if not delivered by Fri, Jan 21, 2011
- I will ask counselors/coaches to assign you detention with me thereafter

- January 10 to February 11, 2011

- Survey results posted in trig section
- With mastery=3, average=2, OMG=1, and WTF?!!!=0, average mastery was between 1.0 and 1.5 (smh)
- I will attempt to provide more scaffolding (support) for you (we now have technology, which might help….)
- Consider your optimal number of problems per night to solve
- You gotta practice!
- I don’t want pre-calculus to be the ruin of your life

- Homework problems limited to no more than 6, but they ARE mandatory and will be collected
- Mandatory means you WILL do them, or stay after school with me to complete them (I will allow some leeway if you let me know about scheduling problems beforehand)
- A moving anecdote </sarcasm mode off>
- PowerPoints will be posted on-line at GHS site
- Give me written suggestions for additional assignments/activities to boost understanding

- Read Chapter 3-1 and 3-2
- (I will not review 3-1 in class but will assume you know it)

- Using Foerster’s requirement that you demonstrate your understanding verbally, graphically, numerically, and algebraically of the following 4 terms: amplitude, cycle, phase displacement, and cycle for a sinusoidal graph

- You will be applying these definitions in an exploration tomorrow.
- You must know how to do inverses, dilations, and transformation from now on (Translation: you won’t pass the class if you can’t do them)
- Everything you learn here is seamlessly connected to everything else

- Definitions of functions and relations
- Identify the 8 different types of functions
- Work with composite functions (define and calculate)
- Be able to perform transformations on any given function:
- Vertical and horizontal translations
- Dilations

- Calculate and graph inverses of functions

- Relation: a RULE which associates some number with a given input
- E.g., x → x2

- Function: relation that assigns only a single value for each input (“vertical line test”)
- Why do we care?

- How to write it:
- Example: g(x)=2x3; f(x) = 2x-3
- f(g(x)) = f(2x3) = 2(2x3)-3 = 4x3 -3
- You must be able to calculate the value at any point AND to be able to write the composite equation!

- Vertical (moving it up or down)
- How to do it?

- Horizontal (moving it back and forth)
- What to we modify?

- Vertical (making it taller or shorter; also making it negative)
- How?

- Horizontal (making it wider or narrower)
- How?

- General formula:
(p. 18 of Foerster)

- “Undoes” what the function does
- Can get it from the graph of the function
- Graphing inverses: rotate 90° counterclockwise, and reflect across y-axis
- Alternatively, reflect across the line y = x

- Calculating inverses: exchange variables
- Example: converting Fahrenheit to centigrade and vice versa

- Reflections across the x-axis
- Ordered pair (x,y) →(x, -y)
- Example (p. 44): f(x) = x2 – 8x + 17
- Reflection g(x) = -f(x)

- Reflections across the y-axis
- Ordered pair (x,y) →(-x, y)
- Reflection g(x) = f(-x)