MHB Determine exact solutions to trig equation with graphing calculator

estex198
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Im trying to determine the exact solutions (in degrees) to the trig equation shown below. I'm only interested in solutions over the interval [0, 360) . In my ti-83+, I input the function as y= 6(1/cos(X))^2*tan(X)-12tan(X). If I already know the number of solutions is 6, how can I tell this from the graph??
 

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estex198 said:
If I already know the number of solutions is 6, how can I tell this from the graph??

Count them?
 
A graph like this may make it easier for you to count the roots:

View attachment 1932
 

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Is that graph plotted using radians? Still it looks like 7.
 
estex198 said:
Is that graph plotted using radians? Still it looks like 7.

Yes, I did not convert to degrees, I just let the domain be $$0\le x<2\pi$$ which means you do not count the root at $x=2\pi$.
 
Ok great! So now I see y=0 (or roots as you refer to them) at 7 points. Thanks for the help!
 
estex198 said:
Ok great! So now I see y=0 (or roots as you refer to them) at 7 points. Thanks for the help!

You don't want to count the root at $x=2\pi$ because this is excluded from the domain.
 
MarkFL said:
You don't want to count the root at $x=2\pi$ because this is excluded from the domain.

Forgive me, I meant to say I see y=0 at 6 points. Thanks for reminding me of the domain.
 

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