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Math Help - Weird basic question

  1. #1
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    Weird basic question

     <br />
sin(x+50)=2cosx<br />

    It's weird that this question doesn't have any special angle or any sort, I don't know how to solve this question with 50^\circ as the angle!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Punch View Post
     <br />
sin(x+50)=2cosx<br />

    It's weird that this question doesn't have any special angle or any sort, I don't know how to solve this question with 50^\circ as the angle!!
    \sin(x+50)=\sin(x)\cos(50)+\cos(x)\sin(50)=2\cos(x  )

    so:

    \tan(x)=\frac{2-\sin(50)}{\cos(50)}

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    \sin(x+50)=\sin(x)\cos(50)+\cos(x)\sin(50)=2\cos(x  )

    so:

    \tan(x)=\frac{2-\sin(50)}{\cos(50)}

    CB
    Thanks but how do I solve for x with this? Also, how did you relate tan(x) with this?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Punch View Post
    Thanks but how do I solve for x with this?
    arctan

    CB
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  5. #5
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    Quote Originally Posted by CaptainBlack View Post
    arctan

    CB
    SOrry but what is arctan?
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  6. #6
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    It is the inverse function to tangent. tan(arctan(x))= x and arctan(tan(x))= x as long as x is between -pi/2 and \pi/2. Also called tan^{-1}(x) which must not be confused with \frac{1}{tan(x)}= cot(x).
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