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How to sketch $y=2\tan(x+\frac{\pi}{4})$ , $x \in (0,2\pi)$

$2\tan$ , 2 is used to be amplitude in $\cos$ and $\sin$ graph but for the $\tan$ there is no amplitude,so where will that $2\tan$ sketch, also

$x+\frac{\pi}{4}=\pi$

$x=\frac{4\pi}{4}-\frac{\pi}{4}$

$x=\frac{3\pi}{4}$

it is right?

Can you please explain me in step by step and show me how to sketch. Thank you so much.

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    [This link](http://mathsisinteresting.blogspot.com/2008/08/how-to-sketch-trigonometric-graph.html) might be useful (and probably many similar can be found easily).2012-05-13

1 Answers 1

2

1) Open any basic calculus, or even trigonometry, book and look and understand the graph of $\tan x$

2) Now "shift" that graph by a rate of $\frac{\pi}{4}$ to the right to get $\tan\left(x+\frac{\pi}{4}\right)$ (thus for ex., for $x=0\,\,$ we'll have now the value that $\tan x$ had at $x=\frac{\pi}{4}$...

3) Finally, multiply every value of $\tan\left(x+\frac{\pi}{4}\right)$ by 2, thus "expanding the graph"

DonAntonio

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    I think you may be right, it looks geometrically more logical to call that a shift to the left.2012-05-13