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Math Help - Could really use some help

  1. #1
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    Could really use some help

    Im at a point in my book where I have to graph functions of sine and cosine
    one such example of the problems is

    Graph 1 cycle and lable 5 points on each.
    F(x)=sin pie x <---- that is "F of X with sine...then the symbol for pie and x next to it

    I know the points and can lable the amplitude and period and I can even graph it on my TI-83 but I am lost when It comes to graphing it by hand ....any help would be great

    another question is
    Solve for all angles over the interval [0,2pie] such that Sin of theta = 1/2

    I have some Ideas and have read the book but I still dont know where to even start with this one either
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  2. #2
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    Quote Originally Posted by mazdatuner
    Im at a point in my book where I have to graph functions of sine and cosine
    one such example of the problems is

    Graph 1 cycle and lable 5 points on each.
    F(x)=sin pie x <---- that is "F of X with sine...then the symbol for pie and x next to it

    I know the points and can lable the amplitude and period and I can even graph it on my TI-83 but I am lost when It comes to graphing it by hand ....any help would be great
    Try doing this, you need to graph f(x)=\sin (\pi x).
    You know you amplitude it 1 and your period is \frac{2\pi}{|\pi|}=2. On this interval [0,2] you midpoint is a zero, meaning x=1 then, f(x)=0. And the mipoints of those, (the quarters of [0,2]) are the max and min (with amplitude 1), thus at x=1/2 and x=3/2 you have a max and min resprectively. Then, you can draw a responable graph knowing this.
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  3. #3
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    Quote Originally Posted by mazdatuner
    Solve for all angles over the interval [0,2pie] such that Sin of theta = 1/2
    First you know that \sin (\pi/6)=1/2.
    But, you still need other solutions on interval [0,2\pi].
    Remember that in the 2nd quadrant the sine is positive. Thus, the other solution appears in the second quadrant. Which is \pi-\pi/6=\frac{5\pi}{6}.
    Hence, the two solutions are,
    \theta=\left\{\begin{array}{c}\pi/6\\ 5\pi/6
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