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Trigonometry determine exact solutions to trig equation with graphing calculator

estex198

New member
Feb 7, 2014
14
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
Jan 26, 2012
1,403

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
A graph like this may make it easier for you to count the roots:

estex198.jpg
 

estex198

New member
Feb 7, 2014
14
Is that graph plotted using radians? Still it looks like 7.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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
Feb 7, 2014
14
Ok great! So now I see y=0 (or roots as you refer to them) at 7 points. Thanks for the help!
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
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

New member
Feb 7, 2014
14
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.