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B What is the use of simplifying a question in math?

  1. May 19, 2017 #1
    Hello. I have been looking into trigonometric identities that helps to simplify a question in mathematics. But the question that I have is, why do I need to simplify a question?

    For instance:
    Sin(x) * Cos(x) means Sin(2*x)/2.
    I have no answer that tells me why I simplify Sin(x) * Cos(x) to its corresponding answer.

    I have plotted graphs of Sin(x) * Cos(x) and Sin(2*x)/2 and both the expression give the same result.

    I request you to write all the words associated with this question.

    Thank you.
     
  2. jcsd
  3. May 19, 2017 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Double-angle formula

    Simplifying the result makes it easier to understand it, it makes comparisons easier, and it is easier to use it in further steps if it is not the final answer.
    The question "what is the nicest answer" is not always easy to answer. It is obvious that ##\displaystyle \left(\frac {3\sin(x)}{2} - \frac {\sin^2(x)}{2\sin(x)}\right) \left(\frac {4\cos^2(x)}{3\cos(x)} - \frac {\cos(x)}{3}\right)## is not a proper final answer, although it is identical to your expression, but sin(x) cos(x) versus sin(2x)/2? I would prefer sin(x) cos(x) over sin(2x)/2 in most cases, unless the double angle (2x) appears elsewhere as well.
     
  4. May 19, 2017 #3

    rock.freak667

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    Homework Helper

    In my experience it is better to put it in the simplest form for ease of future solutions or graph plotting.

    For example say you are asked to plot the long trig expression mfb posted within a certain range and you don't have a plotter. So you are to use excel or some similar spreadsheet program. And if you simplified the expression, it might be something like (it is not though) sin(9x)cos(3x).

    In excel, I'd find it easier to plot sin(9x)cos(3x) than the long expression where I am likely to make a mistake and thus get the final solution wrong.
     
  5. May 19, 2017 #4

    jedishrfu

    Staff: Mentor

    Looking at the sin cos expression its hard to picture its graph but looking at sin 2x I know immediately that it will look like a sin x graph but with a doubled cycle in the domain of 0 to 2pi

    Its the same reason for recasting a linear equation into y = mx + b form so that you can get the y intercept and the slope immediately and can draw the graph.
     
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