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How do you graph # f(x)=1- cos 3x#?

Answer 1

#y=1-cos3x#

#y=Acos[B(x-C)]+D# ( A being amplitude, B being the period, C being the phase shift, and D being the vertical shift).

#y=cos[(3x)]-1#

Two things I can see immediately now that we reorganized the equation is that we have an amplitude of 1 and a vertical shift of -1 (down 1).

Now we will want to find the period using the equation for finding the period for cosines and sin #(2pi)/B#, so the period is #(2pi)/3#. We also see that there is no phase shift. Okay! We have everything we need to graph the equation now.

Amp: 1
Period: (2pi)/3
PS: none
VS: -1

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Answer 2

Anna Andrews

To graph the function ( f(x) = 1 - \cos(3x) ), follow these steps:

Identify the basic cosine function: ( y = \cos(x) ). This function has a period of ( 2\pi ) and oscillates between -1 and 1.
Determine how the basic cosine function has been modified. In this case, the modification is ( 1 - \cos(3x) ), which shifts the cosine function vertically upwards by 1 unit.
Consider the effect of the coefficient inside the cosine function, which is 3 in this case. This coefficient compresses the graph horizontally. The period of the function becomes ( \frac{2\pi}{3} ), indicating that the function completes one cycle every ( \frac{2\pi}{3} ) units of ( x ).
Plot key points on the graph. Start with the critical points for the basic cosine function, which are at ( x = 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi ), and so on. Then, apply the horizontal compression factor of 3 to these points.
Draw the graph by connecting the plotted points. The graph should exhibit a periodic wave that oscillates between ( y = 0 ) and ( y = 2 ), with the peaks and troughs occurring at the adjusted critical points based on the compression factor of 3.

By following these steps, you can accurately graph the function ( f(x) = 1 - \cos(3x) ) and visualize its behavior over the specified interval.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.