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Math Help - How do you find the sin, cos, or tan of a number?

  1. #1
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    How do you find the sin, cos, or tan of a number?

    Specifically something like sinx=-4 and cosx=-1
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  2. #2
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    I think your question is misleading. To find the "sine of a number" you would use a calculator. But from your examples, it seems you want to solve for x, when x is in a trig function.

    Simply take the inverse of the trig function.


     <br />
\cos{x} = \frac{1}{2}<br />
    x = \arccos{\frac{1}{2}}
    x = \frac{\pi}{3}


    The inverse functions are symbolized by the inverse sign, e.g., sin^{-1}.

    Also, if you are not allowed to use a calculator, the you can use a "unit circle" for common angles.
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  3. #3
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    I've read that you can use triangles to solve for inverse functions, but I can't wrap my head around it. I understand how to get <br />
\sin{x} = \frac{1}{2}<br />

    using a special right triangle, but how can you get sinx=-4 using that technique?
    Last edited by capo327; October 7th 2009 at 08:19 PM.
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  4. #4
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    Are you using only real numbers or can you use imaginary numbers for this problem?

    If you are using only real numbers, then sinx = -4 has no real solution, since -1 <= sinx <= 1. So the answer would be "No Solution."

    As for the other example you gave, cosx = -1, that is in the domain of cos, so we can get x = pi.

    Patrick
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  5. #5
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    Thanks a lot, this is really helpful. I think I just have one more question, and that is how to find \cos{\frac{\pi}{2}}=x
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  6. #6
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    Two methods come to mind. My favorite: use a calculator. TI-84 Plus is my personal pick.

    Of course, you can do this one by using the unit circle also. \frac{\pi}{2} is in radians. In degrees, that same angle is 90 degrees. If on a xy plane you draw a line that is at 90 degrees, you are drawing a line straight up. One unit up is at the point (0,1), right? Since cos(t) = x, then we just look at the x value, which is zero. So...

    \cos{\frac{\pi}{2}} = 0

    Patrick
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  7. #7
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    So the best advice for these types of problems is to memorize the unit circle? Thanks for all the help.
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  8. #8
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    I was always told to memorize the unit circle. And I never, ever did. I was able to get by though by using my calculator and by creating the unit circle using simple logic whenever I really needed it. I still don't have most of the basic angles memorized, I always check with my calculator.

    That being said, my advice is to memorize the common angles, as it will really help out in the years to come. I still waste time creating the unit circle when if I just had it memorized it would save me a minute or two.
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