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In the future, remember that the number preceding the cosine function will always be its amplitude. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is. The number is called the vertical shift. The amplitude of is. Replace with in the formula for period. Before we progress, take a look at this video that describes some of the basics of sine and cosine curves. The graph of which function has an amplitude of 3 and a right phase shift of is. The general form for the cosine function is: The amplitude is: The period is: The phase shift is. Ctivity: Graphing Trig Functions [amplitude, period]. The same thing happens for our minimum, at,.
Half of this, or 1, gives us the amplitude of the function. Stretching or shrinking the graph of. In, we get our maximum at, and. Note: all of the above also can be applied. Ask a live tutor for help now. Substitute these values into the general form: The phase shift of the function can be calculated from. We solved the question! The interactive examples. For more information on this visit. Thus, by this analysis, it is clear that the amplitude is 4. Nothing is said about the phase shift and the vertical shift, therefore, we shall assume that.
Therefore, plugging in sine function and equating period of sine function to get. Since the sine function has period, the function. The graph of a sine function has an amplitude of 2, a vertical shift of −3, and a period of 4. Think of the effects this multiplication has on the outputs.
By a factor of k occurs if k >1 and a horizontal shrink by a. factor of k occurs if k < 1. Graphing Sine, Cosine, and Tangent. If, then the graph is. Gauth Tutor Solution. The constants a, b, c and k.. Find the amplitude, period, phase shift and vertical shift of the function. To the cosine function. Provide step-by-step explanations. How do you write an equation of the cosine function with amplitude 3 and period 4π? 3, the period is, the phase shift is, and the vertical shift is 1.
Grade 11 · 2021-06-02. Since our equation begins with, we would simplify the equation: The absolute value of would be. So, the curve has a y-intercept of zero (because it is a sine curve it passes through the origin) and it completes one cycle in 120 degrees. Have amplitude, period, phase shift. The important quantities for this question are the amplitude, given by, and period given by.
A horizontal shrink. This complete cycle goes from to. Covers the range from -1 to 1. This will be demonstrated in the next two sections. The period of the standard cosine function is.
Crop a question and search for answer. Amplitude and Period. Amplitude of the function. Here, we will get 4. Once in that form, all the parameters can be calculated as follows. In this case our function has been multiplied by 4. So this function completes.