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Math Help - Finding solutions within the range?

  1. #1
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    Finding solutions within the range?

    Hi folks,new to the forum and would like to start by asking for help in four trignometry questions,lol!

    As the title says, I have to find all solutions within the given range, Ive been racking my brains all day and can't get anywhere. They are as follows:

    8.2 tan 2x = 10 0< x <180


    5 cos 8 ( θ - 16) = -13 0 < θ < 140



    5 sin 6x = -2 0< x < π



    50 sin (3 θ + π/6) = 30 0< θ <2.5

    π = pi (it doesnt appear to be clear the way ive written it

    any help would be highly appreciated.

    Thanks.
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  2. #2
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    well you do the first one like this:

    8.2 tan 2x = 10 0< x <180

    divide the 8.2 to the other side
    tan 2x = 10/8.2

    take the inverse of tangent which makes it
    tan^-1 (10/8.2) = 2x

    divide the two so your left with x
    and solve with a graphing calculator
    [tan^-1 (10/8.2)]/ 2 = x = 25.324

    then you can check 8.2*tan(2*25.324) = 9.999999 close enough haha
    hope that atleast gets you on the right track
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by Tino1210 View Post


    50 sin (3 θ + π/6) = 30 0< θ <2.5


    Thanks.
    50\sin(3\theta+\frac{\pi}{6})=30

    Divide both sides by 50.

    \sin(3\theta+\frac{\pi}{6})=\frac{3}{5}

    Take arcsin of both sides.

    \sin^{-1}(\sin(3\theta+\frac{\pi}{6}))=\sin^{-1}(\frac{3}{5})

    3\theta+\frac{\pi}{6}=\sin^{-1}(\frac{3}{5})

    Subtract \frac{\pi}{6} from both sides and divide by 3

    \theta=\frac{1}{3}\sin^{-1}(\frac{3}{5})-\frac{\pi}{18}

    \theta=.0399674444 \; \; radians

    Check: 50\sin(3(.0399674444)+\frac{\pi}{6})=30
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