graphing trig functions over the domain 0 to 2pi

•Topic: Sinusoidal Functions
Aim: Graphing the sin and cos function over the domain 0 to 2π

•Do Now: Write the equation for a basic sine function (y = sin x) that is shifted 2 units to the left

•Using the graphing calculator to graph a trig function

•Y = sin x + x

•Domain: 0 to 2π

•Y1 = sin x + x

•Window:

•Xmin = 0

•Xmax = 2π

•Xscl = 1

•Ymin = 0

•Ymax = 10

•Yscl = 2

•Xres = 1 (always)

•Graph

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•Basic sin graph

•Basic sin graph shifted up by x

•The graph begins at the same point as the basic sine curve because the initial value is x = 0. Then it is shifted up by positive values because x is always a positive real number (can you explain why?)

•The graph should be displayed in the first quadrant only (why is this so?)

•Is the graph exhibiting increasing or decreasing behavior over the domain?

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•Practice Problems

       1.  Y = cos x – 2x

•Make sure window is correct

•Analyze the graph using the information that we used to analyze previous trig function.

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          2. Y = sin (x + cos x)

•SAT/ACT Prep

•Handout

•#55, 56, 57

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•#67 - 71

•Exit slip

•Can you describe how a shifted sinusoidal function is used in the real world?

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•Please be specific and write at least one paragraph explaining how the shift clarifies necessary information in your example.

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