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Math Help - Visualizing & solving trig equations

  1. #1
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    Visualizing & solving trig equations

    Find the first 4 positive solutions to each equation. (Use unit circle to make sense of each equation).

    1. sin2\theta=-\frac{1}{2}

    2. cos2\theta=\sqrt{1-sin^2\theta}

    3. cos\left [sin^-1 \frac{1}{2}+cos^-1 \frac{-\sqrt{3}}{2} \right ]
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  2. #2
    Junior Member
    Joined
    Nov 2009
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    Find the first 4 positive solutions to each equation. (Use unit circle to make sense of each equation).

    1.

    2.

    3.

    1. is quite easy, just draw a circle and make it go around twice i.e. 720 degrees. and find values in 3rd/4th quad i.e 210. and equate it too 2@ and solve for 4 positive values. 165,105,285,345

    2. re-arrange the surd thing to get cos2@=cos@, and draw a graph of both and find intersections that are positive. it seems easier to me than using a circle. 0,120,240,x. i didnt bother drawing the rest up

    3. good luck. no idea
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