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Math Help - Finding approximate solutions to equations

  1. #1
    Newbie
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    Arrow Finding approximate solutions to equations

    Dear friends, please explain to me how to solve these problems.
    Thank you!
    1) Approximate to the nearest .1 degree all angles [theta] in the interval [0,360) that satisfy the equation sin(theta)=.7584
    (might be more than one answer)

    2) Approximate to the nearest .01 degree all angles [theta] on the onterval [0, 2pi) that satisfy the equation sin(theta)=.8412

    Thank you!
    Last edited by mr fantastic; January 17th 2010 at 01:06 PM. Reason: Changed post title
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  2. #2
    MHF Contributor
    Joined
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    In a unit circle, the y co-ordinate is Sin{\theta}.

    If this is positive, then the y co-ordinate is above the x-axis.

    If you draw a horizontal line through this y-axis value,
    it cuts the circle in two places.

    Calculating inverse sine gives you the acute angle the point on the circle makes with the positive x-axis.

    As the situation is symmetrical, how do you calculate the answer that
    your calculator does not give you?
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