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8:53 16:10 Suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift YouTubeStart of suggested clipEnd of suggested clip How To Find Amplitude, Period, Phase Shift, & Midline Vertical Shift
If a function has a repeating pattern like sine or cosine, it is called a periodic function. The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. So the period of or is . Any part of the graph that shows this pattern over one period is called a cycle.
0:27 4:50 Suggested clip Trigonometric Functions and Graphing: Amplitude, Period, Vertical YouTubeStart of suggested clipEnd of suggested clip Trigonometric Functions and Graphing: Amplitude, Period, Vertical
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2. So, a coefficient of b=1 is equivalent to a period of 2. To get the period of the sine curve for any coefficient b, just divide 2 by the coefficient b to get the new period of the curve.
The period is the distance between each repeating wave of the function, so from tip to tip of the function's graph. As you can see from this graph, the distance between the tips of the function is 3.034 - 1.463 = 1.57. 1.57 is the same as pi over 2, which is the same as we got from using the formula.
1:59 4:57 Suggested clip Midline, amplitude and period of a function | Graphs of trig functions YouTubeStart of suggested clipEnd of suggested clip Midline, amplitude and period of a function | Graphs of trig functions
Amplitude is the distance between the center line of the function and the top or bottom of the function, and the period is the distance between two peaks of the graph, or the distance it takes for the entire graph to repeat. Using this equation: Amplitude =APeriod =2BHorizontal shift to the left =CVertical shift =D.
The period of the sine curve is the length of one cycle of the curve. The natural period of the sine curve is 2. So, a coefficient of b=1 is equivalent to a period of 2. To get the period of the sine curve for any coefficient b, just divide 2 by the coefficient b to get the new period of the curve.
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