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How do you graph #cos^2 x# and #sin^2 x#?

Answer 1

See below

Of course, without some graphic tool, you can't make an exact graph, so I'll tell you the ideas which allow you, knowing the graphs of #cos(x)# and #sin(x)#, to sketch those of their squares.

So, if you start from the graph of #cos(x)#, for example, you know that #cos^2(x)# will have the same zeroes and the same maxima. Also, all the minima becomes maxima, because #(-1)^2=1#.

This is everything you can calculate perfectly. Once you have these break points, you must connect them with a line that resembles the one of #cos(x)#, and you can't to anything more precise

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Answer 2

Caroline Adams

To graph ( \cos^2(x) ) and ( \sin^2(x) ), you can follow these steps:

Determine the period of the functions. Since ( \cos^2(x) ) and ( \sin^2(x) ) are both squared trigonometric functions, they have the same period as their respective trigonometric functions ( \cos(x) ) and ( \sin(x) ), which is ( 2\pi ).
Identify key points within one period. For ( \cos^2(x) ) and ( \sin^2(x) ), you can plot points for ( x = 0 ), ( x = \frac{\pi}{2} ), ( x = \pi ), ( x = \frac{3\pi}{2} ), and ( x = 2\pi ).
Calculate the function values at these key points. Evaluate ( \cos^2(x) ) and ( \sin^2(x) ) at the identified key points.
Plot the points on the coordinate plane. Mark the points corresponding to the function values obtained in step 3.
Connect the points with smooth curves. Since ( \cos^2(x) ) and ( \sin^2(x) ) are continuous functions, draw smooth curves passing through the plotted points to represent the graphs of the functions.
Repeat the process for each period. Since the period of ( \cos^2(x) ) and ( \sin^2(x) ) is ( 2\pi ), you can repeat the same steps for additional periods if necessary.

By following these steps, you can graph ( \cos^2(x) ) and ( \sin^2(x) ) accurately on the coordinate plane.

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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.