Trigonometry pre calculus
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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

Trigonometry/Pre-calculus

January 10, 2011


Warm up exercises

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

Welcome back!

  • 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


Hartley s responses to your concerns algebra 2 survey

Hartley’s responses to your concerns/algebra 2 survey

  • 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


Immediate adjustments

Immediate adjustments

  • 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


Homework

Homework

  • 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

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


Outline of function review what you need to know and master

Outline of function review (What you need to know and master)

  • 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

Basic concepts

  • 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

Composite functions

  • 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

Transformations

  • Vertical (moving it up or down)

    • How to do it?

  • Horizontal (moving it back and forth)

    • What to we modify?


Dilations

Dilations

  • 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

Inverses

  • “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

Reflections (Chapter 1-6)

  • 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)


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