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21 Cards in this Set
- Front
- Back
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Definition of a periodic function |
function that repeats itself over regular intervals (cycles) of its domain |
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the length of an interval in a function that repeats itself is called the |
period |
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the graphs of trigonometric functions y = sin x and y = cos x are |
sinusoidal curves |
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Define the amplitude of a periodic function |
half the distance between the maximum and minimum values of the function // the vertical stretch // vertical distance the curve is above or below the midline |
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amplitude is always _______ |
positive |
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formula to determine amplitude |
max - min / 2 |
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does a tangent function have an amplitude? |
no |
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the period is a ______ stretch about the _____ axis |
horizontal, y |
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period for cosine and sine functions |
2pi / lbl or 360 / lbl |
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period for tangent functions |
pi / b or 180 / b |
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when given function such as sinbx, cosbx or tanbx determine period by |
replacing b with value and simplifying |
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if b > 1 the period is _______ than 2pi |
less |
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if 0 < b < 1 the period is ______ than 2pi |
greater |
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vertical translation of the graph of a periodic function is called a |
vertical displacement |
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formula to determine vertical displacement is |
max + min / 2 |
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horizontal translation of the graph of a periodic function is called a |
phase shift |
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the graph of sinx |
rises |
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the graph of cosx |
falls |
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when looking for phase shift of a cos function look for a |
maximum point |
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when looking for a phase shift of a sine function look for a |
zero |
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when writing equations for a sine and cosine function the only thing that differs is the |
phase shift
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