# $\cot(x)$ or $\tan(x)$ amplitude with $F(x)$ or $G(x)$?

If you are doing $f(x)$ and $g(x)$ of a tangent/cotangent function and you get an amplitude. Should you write the final equation with or without the amplitude because technically tan and cot don't have amplitudes.

i.e. $$F(x) = \cot x + 1$$ $$G(x) = 3f(x+3) + 1$$ $$G(x) = 3\cot(x+3) + 2$$

Would you write $G(x) = \cot(x+3) + 2$ because there is no amplitude?

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I'm not too sure what the problem is asking. It would be great if you could clarify. What is $f(x)$? What is $g(x)$? –  EuYu Nov 19 '12 at 14:54
If you already have $G(x)=3cot(x+3)+2$ then you cannot simply drop the 3 in front, or you change the function. For sine and cosine, the number in front (its absolute value) is the amplitude. As you say, tan and cot don't really have them, but the size of the multiplier has something to do with the shape of the graph. 3cot(x+3)+2 is three times more expanded around y=2 than is cot(x+3)+2. –  coffeemath Nov 20 '12 at 1:16