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

Question

Anna Andrews · Accepted Answer

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

Caroline Adams · Answer

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

1. 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 $.

2. 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 $.

3. Calculate the function values at these key points. Evaluate $ \cos^2(x) $ and $ \sin^2(x) $ at the identified key points.

4. Plot the points on the coordinate plane. Mark the points corresponding to the function values obtained in step 3.

5. 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.

6. 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.