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

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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!

  • 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

  • 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

  • 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

  • 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


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

  • 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

  • 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

  • Vertical (moving it up or down)

    • How to do it?

  • Horizontal (moving it back and forth)

    • What to we modify?


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

  • “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 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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