•Topic:
Sinusoidal Functions
Aim: Graphing the sin and cos function over the domain 0 to 2π
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
•
•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?
•
•
•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.
•
2. Y = sin (x + cos x)
•SAT/ACT
Prep
•Handout
•#55,
56, 57
•
•#67 -
71
•Exit
slip
•Can
you describe how a shifted sinusoidal function is used in the real world?
•
•Please
be specific and write at least one paragraph explaining how the shift clarifies
necessary information in your example.
•
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