Trigonometrydetermine exact solutions to trig equation with graphing calculator

estex198

New member
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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Prove It

Well-known member
MHB Math Helper
If I already know the number of solutions is 6, how can I tell this from the graph??
Count them?

MarkFL

Staff member
A graph like this may make it easier for you to count the roots:

estex198

New member
Is that graph plotted using radians? Still it looks like 7.

MarkFL

Staff member
Is that graph plotted using radians? Still it looks like 7.
Yes, I did not convert to degrees, I just let the domain be $$\displaystyle 0\le x<2\pi$$ which means you do not count the root at $x=2\pi$.

estex198

New member
Ok great! So now I see y=0 (or roots as you refer to them) at 7 points. Thanks for the help!

MarkFL

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