# Math Help - Trig. Graphs

1. ## Trig. Graphs

Hi

How do I actually sketch a trig. graph of the form y = A sin(x +/- a), y = A cos (x +/- a), and y = 1 +/- tan x. Do I simply draw the graphs when there is only one sign and put them onto one graph?

Thanx

2. ## Sketching trig graphs

Hello xwrathbringerx
Originally Posted by xwrathbringerx
Hi

How do I actually sketch a trig. graph of the form y = A sin(x +/- a), y = A cos (x +/- a), and y = 1 +/- tan x. Do I simply draw the graphs when there is only one sign and put them onto one graph?

Thanx
If I had asked for a sketch of the graph of $y = A \sin(x-a)$, I would expect to see a diagram showing:

• $x-$ and $y-$axes, including both positive and negative values of $x$ and $y$.
• a sine wave centred on $Ox$, showing at least part of a cycle for negative values of $x$, and at least, say, one-and-a-half cycles for positive $x$.
• points $(0,A)$ and $(0,-A)$ marked on $Oy$, with the sine wave having corresponding maximum and minimum values
• an indication on the diagram of the phase shift, given by the value of $a$; in other words, the sine wave passing through a point marked as $(a,0)$.

I think I'd also expect to see some reference to the fact that the diagram shows the case where $A>0$ and $a>0$.

For a fuller answer, you could obviously also sketch what happens if either or both of $A$ and $a$ is negative. Clearly, there would then no need to consider separately the graph of $y = A \sin(x+a)$.

Similarly with $A \cos(x-a)$.

With $y = 1 \pm \tan x$, I think I would expect on a single graph a sketch showing $y = \tan x$ (perhaps drawn as a broken line), and then an indication that $y = 1+\tan x$ shifts this graph 1 unit in the y-direction.

It would probably be too confusing to add $y = 1 - \tan x$ to this same sketch, unless you used several colours. So, as a separate sketch, I should draw (lightly) $y = -\tan x$, and again shift this 1 unit in the y-direction.

But that's only my opinion...