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Graphing trig functions without calculus

  1. Oct 25, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm in a first-year analysis course, and this question was given by my prof. as practice for her midterm test.

    "Sketch the graph of the function

    [tex]
    \begin{equation*}
    f(x) = \text{sin} 2x + \sqrt{3} \text{cos} 2x
    \end{equation*}
    [/tex]

    Determine the amplitude, the frequency and the phase of [tex]f(x)[/tex].

    2. Relevant equations



    3. The attempt at a solution

    It's been a really long time since I've done graphing transformations of trig functions without calculus, so I truthfully don't remember how to do this.

    I can see they both have period pi, and sin(2x) has amplitude 1 and sqrt3 cos(2x) has amplitude of sqrt3.

    I don't know how to determine the highest point on the graph (amplitude), and I don't know how to determine the phase.

    Thanks for your help.
     
    Last edited: Oct 25, 2009
  2. jcsd
  3. Oct 25, 2009 #2

    Dick

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  4. Oct 25, 2009 #3
  5. Oct 25, 2009 #4
    Last edited: Oct 25, 2009
  6. Oct 25, 2009 #5

    Dick

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