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Trigonometry/Pre-calculus

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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  1. Trigonometry/Pre-calculus January 10, 2011

  2. 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°

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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?

  10. 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!

  11. Transformations • Vertical (moving it up or down) • How to do it? • Horizontal (moving it back and forth) • What to we modify?

  12. 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)

  13. 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

  14. 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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