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Math Help - Simple Trig Identity Question

  1. #1
    Newbie roflcoptur's Avatar
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    Simple Trig Identity Question

    I have basic knowledge of identities.

    Solve each equation for theta if zero degrees is less than or equal to theta is less than or equal to 360 degrees.

    1. 4sin theta - 3csc theta = 0
    2. sec theta - 2tan theta = 0
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  2. #2
    Senior Member pacman's Avatar
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    (1)4sin theta - 3csc theta = 0 --> 4 sin x - 3 csc x = 0;

    4 sin x - 3(1/sin x) = 0,

    (4 sin^2 x - 3)/sin x = 0,

    4 sin^2 x - 3 = 0,

    4 sin^2 x = 3,

    sin^2 x - 3/4 = 0, factoring it.

    (sin x + (sqrt 3)/2)(sin x - (sqrt 3)/2) = 0, the roots are

    sin x = (sqrt 3)/2, -(sqrt 3)/2.

    x = arcsin ((sqrt 3)/2, -(sqrt 3)/2)

    x = {60, 120, 240, 300 degrees} or {pi/3, 2pi/3, 4pi/3, 5pi/3}
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  3. #3
    Senior Member pacman's Avatar
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    4 sin x - 3 csc x = 0; for x = 0 to 360 degrees. The graph is shown below to check for the roots
    Attached Thumbnails Attached Thumbnails Simple Trig Identity Question-aqwwert.gif  
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  4. #4
    MHF Contributor
    Grandad's Avatar
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    Hello roflcoptur
    Quote Originally Posted by roflcoptur View Post
    ...
    2. sec theta - 2tan theta = 0
    \sec\theta -2\tan\theta=0

    \Rightarrow \frac{1}{\cos\theta}-\frac{2\sin\theta}{\cos\theta}=0

    \Rightarrow \frac{1-2\sin\theta}{\cos\theta}=0

    \Rightarrow 1-2\sin\theta=0

    \Rightarrow \sin\theta = \tfrac12

    \Rightarrow \theta = 30^o, 150^o

    Grandad
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