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Math Help - [SOLVED] Inverse Trigonometric Functions

  1. #1
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    [SOLVED] Inverse Trigonometric Functions

    Question:
    How to do the inverse trigonometric function to find the exact value of:-
     \arcsin\frac{1}{2}

    Attempt:
    I can do it using a calculator, but I don't know how to find it in the sine function graph ( I know how to draw the graph but I don't know what to do next)


    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question:
    How to do the inverse trigonometric function to find the exact value of:-
     \arcsin\frac{1}{2}
    By definition, \sin^{-1}\left(\frac{1}{2}\right)\, =\, \theta means that \sin\left(\theta\right)\, =\, \frac{1}{2}. For which value of \theta is the value of sine equal to one-half?
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  3. #3
    Newbie mintsmike's Avatar
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    To find the solutions on the sine graph, draw a straight line at x = (1/2). The intersections will be your solutions.

    .

    Hope that this helps,
    mintsmike
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  4. #4
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    Quote Originally Posted by stapel View Post
    By definition, \sin^{-1}\left(\frac{1}{2}\right)\, =\, \theta means that \sin\left(\theta\right)\, =\, \frac{1}{2}. For which value of \theta is the value of sine equal to one-half?
    I know the value but can you please show me the graph and how did you get the value from the graph?

    Thank you
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  5. #5
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    Quote Originally Posted by mj.alawami View Post
    I know the value but can you please show me the graph and how did you get the value from the graph?

    Thank you

     sin^{-1} 0.5 is 30, as you clearly know. If you are familiar with the graph of  y = sinx , then you can draw this and the line that you draw from 0.5 on the x-axis will meet at 30 degrees on the y-axis.
    The graph can be shown here:
    http://www.quickmath.com/www02/image...t/example4.gif
    On the graph, take 3 as the value of 180 and hence 1 as 60. You can see that if you drew a line from 0.5, it would meet halfway to 1 - which is 30!

    I hope this helps you in what you're trying to do!
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