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This may be somewhat of a basic question, but I need to know... I'm trying to find the minimum and maximum for the following: $$y = \frac{\cos 3x}{5}+\sin 3x$$

How is this done on a TI-83?

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Thanks, Thomas, I figured out what was wrong: I had one of the plots under stat plots turned on so it wouldn't let me graph... –  Brandt Oct 23 '12 at 20:16
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1 Answer 1

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  • You enter the function as (for example) a $Y_1$ (using the [y=] button).
  • You try to sketch the graph and adjust the window so that it shows the minimum or maximum that you want to find. (Hint: try for example $x_{min} = -5$, $x_{max} = 5$, $y_{min} = -2$, $y_{max} = 2$)

  • You click [2nd] [calc] and choose (say) minimum.

  • You put the cursor to the left of the minimum and click enter. You put it to the right and click enter.

  • You move the cursor so that it is close to where the minimum is and you click enter.

Note i your case, you will have infinitely many maximums and minimums since he function is periodic. When you find say a minimum, then you can add any (integer) multiple of $\frac{2\pi}{3}$ to get the other minimums. This should be clear from the graph.

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I'm having a problem...when I plug cos(3X/5+sin(3X)) into y1 I get a window range error? –  Brandt Oct 23 '12 at 15:11
    
@Brandt: From the way that you had written things, I assumed that your function was $y = \cos(3x)/5 + \sin(3x).$ To correct the window issue press [window] and set the min and max values to what I have suggested in my answer. –  Thomas Oct 23 '12 at 15:14
    
you're right; I wrote the function incorrectly. But even after correcting that and setting the min and max values to what you suggested I still get an error, this time an "invalid dimensions" error... –  Brandt Oct 23 '12 at 15:22
    
What are the min and max values under [window] ? –  Thomas Oct 23 '12 at 15:23
    
Xmin=-5, Xmax=5, Xscl=-2 (I don't know how to clear this one), Ymin=-2, Ymax=2, Yscl=.1 and Xres=1 –  Brandt Oct 23 '12 at 15:26
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