## How to find the equation for a tangent/cotangent graph?

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.
Lithium
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Joined: Sat May 21, 2011 9:37 pm
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### How to find the equation for a tangent/cotangent graph?

Hi! I'm having a bit of trouble figuring out the equations for this graph.

The graph increases from left to right, so I assumed it a tangent graph. We need to find 2 equations for this graph.
I found the tangent equation but I'm not sure if I did it the right way: first I found the vertical displacement and the phase shift that are pretty obvious on the graph, then since a tangent graph's period is pi not 2pi like that of cosine and sine graphs, and the period on this graph is 2pi, the frequency (or B) is 1/2
Then it seems like the graph has been vertically compressed, so I found a point on the graph (8pi/9,0) and solved for the amplitude (A)
my tangent equation is y=0.24tan((x+0.25pi)/2)+1
I did the same thing for the cotangent graph, but then the cotangent graph is a mirror image of the tangent graph and I can't use reflections since the graph doesn't reflect off the y-axis. So now I'm stuck with only one equation, any idea how I can find the second equation?
Thanks lots!

little_dragon
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Joined: Mon Dec 08, 2008 5:18 pm
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### Re: How to find the equation for a tangent/cotangent graph?

what if u do a "-" insde the cotan? that turns the graph around & then u can shift