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
Hello xwrathbringerx
If I had asked for a sketch of the graph of $\displaystyle y = A \sin(x-a)$, I would expect to see a diagram showing:
- $\displaystyle x-$ and $\displaystyle y-$axes, including both positive and negative values of $\displaystyle x$ and $\displaystyle y$.
- a sine wave centred on $\displaystyle Ox$, showing at least part of a cycle for negative values of $\displaystyle x$, and at least, say, one-and-a-half cycles for positive $\displaystyle x$.
- points $\displaystyle (0,A)$ and $\displaystyle (0,-A)$ marked on $\displaystyle Oy$, with the sine wave having corresponding maximum and minimum values
- an indication on the diagram of the phase shift, given by the value of $\displaystyle a$; in other words, the sine wave passing through a point marked as $\displaystyle (a,0)$.
I think I'd also expect to see some reference to the fact that the diagram shows the case where $\displaystyle A>0$ and $\displaystyle a>0$.
For a fuller answer, you could obviously also sketch what happens if either or both of $\displaystyle A$ and $\displaystyle a$ is negative. Clearly, there would then no need to consider separately the graph of $\displaystyle y = A \sin(x+a)$.
Similarly with $\displaystyle A \cos(x-a)$.
With $\displaystyle y = 1 \pm \tan x$, I think I would expect on a single graph a sketch showing $\displaystyle y = \tan x$ (perhaps drawn as a broken line), and then an indication that $\displaystyle y = 1+\tan x$ shifts this graph 1 unit in the y-direction.
It would probably be too confusing to add $\displaystyle y = 1 - \tan x$ to this same sketch, unless you used several colours. So, as a separate sketch, I should draw (lightly) $\displaystyle y = -\tan x$, and again shift this 1 unit in the y-direction.
But that's only my opinion...
Grandad