Determine exact solutions to trig equation with graphing calculator

[estex198]

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??

 

[Prove It]

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

Count them?

 

[MarkFL]

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

View attachment 1932

 

[estex198]

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

 

[MarkFL]

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]

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

 

[MarkFL]

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.

 

[estex198]

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.