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Math Help - Sum and difference identitiees?

  1. #1
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    Sum and difference identitiees?

    Hello! I have two problems I need help on.
    use sum or difference to find the exact value of each trigonometric function.

    cot 113pi/12
    I know this equals= 4(360)+255
    and 255 is 210+45

    So I did
    cot(210)+cot(45)/(1-cot(210)(cot45)
    Which gives me -3.739 But I am quite sure this is wrong.

    my second problem is
    cos(x+y)= tanx(5/3) and sin y=1/3
    I am quite confused on this one

    Can anyone help me with these problems?
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  2. #2
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    Also for my second problem it has to be between 0<x<pi/2 0<y<pi/2
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  3. #3
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    Quote Originally Posted by homeylova223 View Post
    cot 113pi/12
    I know this equals= 4(360)+255
    and 255 is 210+45
    The period for \displaystyle \tan\theta is \displaystyle \pi not \displaystyle 2\pi

    \displaystyle \cot \left(\frac{113\pi}{12}\right) = \frac{1}{\tan \left(\frac{113\pi}{12}\right)} =  \frac{1}{\tan \left(\frac{(108+5)\pi}{12}\right)}=  \frac{1}{\tan \left(\frac{5\pi}{12}\right)}

    Then use the difference formula on the following.

    \displaystyle \tan \left(\frac{5\pi}{12}  \right)=\tan \left(\frac{8\pi-3\pi}{12}  \right)=\tan \left(\frac{8\pi}{12}-\frac{3\pi}{12}  \right)=\tan \left(\frac{2\pi}{3}-\frac{\pi}{4}  \right)=\dots
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  4. #4
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    I have another quick question well actually 2
    My first one is to find the sec(1275 degrees)
    I have sec(1275)= 3(360)+195
    sec(135)sec(60)+csc(135)csc(60)
    I got -1.193 Did I do this one right?

    On my second problem
    cos(x+y)= tanx(5/3) and sin y=1/3
    I did square root 1-(1/3)^2 and I got cosy= .942

    Then I solved the triangle using tanx(5/3) and I got cosx=.514

    I know siny= 1/3

    So I did square root 1-.514^2 and got sinx= .8577

    So I guess to find answer I must do cos(.514)cos(.942)+sin(.8577)sin(1/3)?
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