# 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.