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Math Help - Trig. Graphs

  1. #1
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    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
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  2. #2
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    Sketching trig graphs

    Hello xwrathbringerx
    Quote Originally Posted by xwrathbringerx View Post
    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...

    Grandad
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