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Day 1 Sine and Cosine Graph notes.notebook
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February 26, 2018
Graphing Sine and Cosine
Using the values you got on the charts from yesterday's "Are You Ready" worksheet, graph the Sine and Cosine functions on a white board with your group. Make these as accurate as you can and go from (360o to 360o) on your x axis.
Day 1 Sine and Cosine Graph notes.notebook
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xaxis
Write in the corresponding radian measures to go with the angles given.
The domain of these two functions is (∞, +∞).
The range of these two functions is ( ).
The x intercepts of the two functions are different:cosine = __________________sine = __________________
The yintercept of the two functions is also different:cosine = __________________sine = __________________
Both of the functions are continuous (as their are no breaks in the graphs)
Both of the functions have some symmetry in them.cosine = __________________sine = __________________
There are some extrema in the two graphs. The maximum is at ______ and the minimum is at ____.
The end behaviors do not exist as both graphs are a constant wave motion.
Both graphs oscillate between 1 and +1.
co
Day 1 Sine and Cosine Graph notes.notebook
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xaxis
More terminology:
The amplitude is defined as being half the distance between the max and min values of the function.(Both of these functions have an amplitude of 1)
The period is defined as being the distance between any two sets of repeating points on the graph of the function.(the period of sine and cosine is 2π)
A phase shift is the difference between the HORIZONTAL position of the function and that of an otherwise similar sinusoidal function. (for example: the sine wave and cosine wave are very similar. How many units would you have to move the cosine wave (horizontally) so that it would match up with the sine wave?)
The frequency is the number of cycles the function completes in a one unit interval. It is the reciprocal of the period.
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General Form of Sine and Cosine Functions
Each of the letters in the functions helps us determine something about its graph.
= amplitude
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f(x) = 3 sin(x + π ) 2
f(x) = 2 cos 3 (x + π/2)5
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Graphing Order1) Amplitude
2) Reflection over x axis
3)
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Practice:
Amplitude: Period:
Freq: Phase Shift:
Midline: Vert. Shift:
Amplitude: Period:
Freq: Phase Shift:
Midline: Vert. Shift:
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