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Math Help - Solving the Sine Equation

  1. #1
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    Question Solving the Sine Equation

    solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)
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  2. #2
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    Quote Originally Posted by SoYah View Post
    solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)
     \sin(x) = \frac{1}{5}

    On way to solve this is to write:

     x = \arcsin(\frac{1}{5}) , and simplify plug it into your calculator.

    Another way is to consider a triangle. If you take the sin of an angle in a triangle, it gives the ratio of the length of the side opposite that angle and the hypotenuse.

    Hence the hypotenuse of our triangle is 5, and the opposite side from angle x is 1. From pythagorus we calculate that the side adjacent to the angle x is  2\sqrt{6}

    Now you know all lengths, you can work out the angle using the cosine rule.
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