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4.2 Period, Amplitude & Phase Shift

4.2 Period, Amplitude & Phase Shift. A Sinusoidal Function. a, b, c, and d all represent values that affect the basic sine curve in different ways *it doesn’t HAVE to be sine…. could be cosine too!. Amplitude : If a periodic function has a max value M and a min value m, then amplitude is

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4.2 Period, Amplitude & Phase Shift

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  1. 4.2 Period, Amplitude & Phase Shift

  2. A Sinusoidal Function a, b, c, and d all represent values that affect the basic sine curve in different ways *it doesn’t HAVE to be sine…. could be cosine too! Amplitude: If a periodic function has a max value M and a min value m, then amplitude is  aka: half the range/ vertical spread

  3. Period: how long it takes to complete 1 cycle Since the period of sine & cosine are both 2π, determines the factor it is dilated horizontally For is amplitude and is period The zeros of a graph occur when y = 0. To find them, set your equation equal to 0 Local maximums occur when the graph changes from rising to falling Local minimums occur when it changes from falling to rising

  4. Ex 1) Graph a b b c a d = = 0 = –2 = 0 1st tick mark Check Period: 2 Amp = Per: IL: 0 –2 a = –2  reflect across x-axis

  5. Ex 1 cont) Find at least two zeros: argument Find local max: cosine has max’s at 0, 2π, etc. Set ‘argument’ = to these Find local min: cosine has mins at π, 3π, etc. Set ‘argument’ = to these Let’s confirm with our graph!

  6. Ex 1) Graph Max 2 Fix it in your notes!!! –2 Zero Zero min min We were wrong about Max & mins… WHY??? a = –2  reflect across x-axis  Changes Max’s to mins & mins to Max’s

  7. PhaseShifts & VerticalShifts *opposite of c horizontal shift (left/ right) *d is it vertical shift (up/ down)

  8. Ex 2) Graph Factor out b b c a d = = = 4 = –2 Check Period: 1st tick mark 4 2 –2 Per = IL: –4 –6 (easier to add to c) Check a point:

  9. Ex 3) Determine equation from the graph. 1 When x = 0, y = –2 then starts to climb, so use –1 Max = –.5 min = –3.5 –2 –4 Per = a max to a max d b a and shift down 2

  10. Homework • #402 Pg 197 #23, 27, 29, 31 – 34, 36 –45, 49 – 54 all When they ask for frequency, Don’t ignore “word problems”! They give you the equation!!! (Super easy!)

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