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Math Help - Trigonometry Equations? multiples of pi?

  1. #1
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    Trigonometry Equations? multiples of pi?

    how would i go about solving this question?

    Solve the following equations in the interval [0, 2pi]. Give the answer as a multiple of pi. Do not use decimal numbers. The answer should be a fraction or an integer.

    sin(t) = -(sqrt(3))/2
    t = __?__ pi

    sin(t) = -1/2
    t = __?__ pi
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  2. #2
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    Do you know the unit circle?
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  3. #3
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    Solve for the basic angle , where all solutions are positive, then use symmetry to evaluate the negative answers - sine is negative in the 3rd and 4th quadrants.
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  4. #4
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    Basic angle(B) = arcsin(sqrt3/2)
    When you have derived the basic angle, check the quadrants in which sin is negative( 3rd and 4th) and hence the solutions are pi+ B and 2pi - B

    Do the same for the 2nd question.
    You may want to draw the quadrants to help you visualise and understand the problem better.

    Hope this helps.
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