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# Trigonometry/Pre-calculus - PowerPoint PPT Presentation

Trigonometry/Pre-calculus. January 10, 2011. Warm-up exercises. 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°. Welcome back!.

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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

• 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

Note! (Achtung!)

• 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

Basic concepts master)

• 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?

Composite functions master)

• 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!

Transformations master)

• Vertical (moving it up or down)

• How to do it?

• Horizontal (moving it back and forth)

• What to we modify?

Dilations master)

• Vertical (making it taller or shorter; also making it negative)

• How?

• Horizontal (making it wider or narrower)

• How?

• General formula:

(p. 18 of Foerster)

Inverses master)

• “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 (Chapter 1-6) master)

• 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)