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How to Graph Period Release

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Changing the Period of the Sine Function The period of the basic sine function y = sin(x) is 2, but if x is multiplied by a constant, that can change the value of the period. If x is multiplied by a number greater than 1, that “speeds up” the function, and the period will be smaller.
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.
The period of the parent graphs of sine and cosine is 2 multiplied by pi, which is once around the unit circle. This action affects the period of the trig function graph. For example, f(x) = sin 2x makes the graph repeat itself twice in the same amount of time. In other words, the graph moves twice as fast.
The period of sin is 2. So sin(2x+2)=sin(2x) for all x.
The period of a periodic function is the interval of x-values on which the cycle of the graph that's repeated in both directions lies. Therefore, in the case of the basic cosine function, f(x) = cos(x), the period is 2.
The period of the graph is, as is the period of. The effect of the negative sign on the inside is to replace x-values by their opposites. This will flip the graph around the y-axis. However, because the graph of cosine is symmetric about the y-axis, this has no effect at all.
0:45 5:26 Suggested clip Ma 113: A graph with a negative amplitude, frequency change, and YouTubeStart of suggested client of suggested clip Ma 113: A graph with a negative amplitude, frequency change, and
What happens when b has a negative value? The difference with a negative value of b however, is our sine curves have the same period as the positive values of b above, but now they are reflected across the x-axis. For a direct comparison between positive and negative values of b, click here.
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