pre-cal 40s february 17, 2009
DESCRIPTION
Graphing sine and cosine functions.TRANSCRIPT
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Contemplating The Wave
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Also see Dave's short course on trigonometry.
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The sine function ... why does it look like this?
fooplot is an online graphing calculator
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The cosine function ... why does it look like this?
fooplot an online graphing calculator
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Graphing Trig Functionsƒ(x) = AcosB(x - C) + Dƒ(x) = AsinB(x - C) + D
The Role of Parameter A
|A|is called the Amplitude
determines the distance of the maximum and minimum values from the Sinusoidal Axis
Acontinues ...
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The graph is stretched A units.
0 <| A | < 1 the graph is compressed by factor A.A < 0 the graph is reflected over the sinusoidal axis.
The role of Parameter B.B is not the period. B determines the period according to this relation:
The period is the distance along the x-axis required to make one "wave".
or
| A | > 1
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The role of parameter C.C is called the phase shift. (aka the horizontal shift)C > 0 the graph is shifted to the right C unitsC < 0 the graph is shifted left C units
WARNING: watch the sign of C
The role of parameter D.D is called the vertical shift, aka average value.D determines the sinusoidal axis.D > 0 the graph shifts up D unitsD < 0 the graph shifts down D units
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Sketch each of the following graphs without using a calculator ...
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What else can we do to the cosine (or sine) function?
fooplot an online graphing calculator
ƒ(x) = AcosB(x - C) + Dƒ(x) = AsinB(x - C) + D
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Now, put what you've learned together, graph this function ...
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Graph this:
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Use the questions on the following slides to practice what you've learned today.
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Solve ...
where 90° ≤ x < 270°
on the interval [π, 2π]
for x ∈ R
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Find the exact value of each of the following ...
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Sketch each of the following graphs without using a calculator ...
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Sketch the following graphs without using a calculator ...
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Sketch the following graphs without using a calculator ...
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Sketch the following graphs without using a calculator ...
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Sketch each of the following graphs without using a calculator ...
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Now, put what you've learned together, graph this function ...