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Math Help - Identity? issues

  1. #1
    Member M670's Avatar
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    Identity? issues

    Simplify and write the trigonometric expression in terms of sine and cosine:

    ?



    So I came up with this
    = 1/f(u)

    But I am not sure what to do or if I am right?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Identity? issues

    I believe what you being asked to do is:

    \tan(u)+\cot(u)=\frac{\sin(u)}{\cos(u)}+\frac{\cos  (u)}{\sin(u)}=?=\frac{1}{f(u)}

    Where the "?" is, combine terms, and you will get the desired form.
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  3. #3
    Member M670's Avatar
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    Re: Identity? issues

    Can you explain what cofunction identities are?


    Identity? issues-cofunction.jpg
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Identity? issues

    Basically, if you have two complementary angles \alpha and \beta, i.e.:

    \alpha+\beta=\frac{\pi}{2}

    then a trig. function whose argument is one of the angles will be equal to its co-function evaluated at the other. That is:

    \sin(\alpha)=\cos(\beta)

    \cos(\alpha)=\sin(\beta)

    \tan(\alpha)=\cot(\beta)

    \cot(\alpha)=\tan(\beta)

    \sec(\alpha)=\csc(\beta)

    \csc(\alpha)=\sec(\beta)
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  5. #5
    Member M670's Avatar
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    Re: Identity? issues

    Quote Originally Posted by MarkFL2 View Post
    I believe what you being asked to do is:

    \tan(u)+\cot(u)=\frac{\sin(u)}{\cos(u)}+\frac{\cos  (u)}{\sin(u)}=?=\frac{1}{f(u)}

    Where the "?" is, combine terms, and you will get the desired form.
    Oh does this work out to Sin^2(u)+Cos^2(u) which would equal 1?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Identity? issues

    Yes, that would be the numerator...what is the common denominator, which is what f(u) is?
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  7. #7
    Member M670's Avatar
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    Re: Identity? issues

    Quote Originally Posted by MarkFL2 View Post
    Yes, that would be the numerator...what is the common denominator, which is what f(u) is?
    I am not understanding this ? if I found the numerator to be 1 this means 1=1/f(u)?
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  8. #8
    MHF Contributor MarkFL's Avatar
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    Re: Identity? issues

    When you combine the two terms, the numerator simplifies to 1, but there is also the denominator.
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  9. #9
    Member M670's Avatar
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    Re: Identity? issues

    I really don't know I am now lost.. I understand what you said, I just can't wrap my mind around this one...
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  10. #10
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    Re: Identity? issues

    \frac{\sin{u}}{\cos{u}} + \frac{\cos{u}}{\sin{u}} = \frac{\sin^2{u}+\cos^2{u}}{\sin{u}\cos{u}} = \frac{1}{\sin{u}\cos{u}}
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  11. #11
    Member M670's Avatar
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    Re: Identity? issues

    Quote Originally Posted by skeeter View Post
    \frac{\sin{u}}{\cos{u}} + \frac{\cos{u}}{\sin{u}} = \frac{\sin^2{u}+\cos^2{u}}{\sin{u}\cos{u}} = \frac{1}{\sin{u}\cos{u}}
    I know my biggest problem is my algebra skill set is very poor right now.... Can you break this down into a few more steps for me to be able to understand even better?
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  12. #12
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    Re: Identity? issues

    \frac{a}{b} + \frac{b}{a}

    common denominator is a \cdot b

    \frac{a \cdot a}{a \cdot b} + \frac{b \cdot b}{a \cdot b}

    \frac{a^2}{ab} + \frac{b^2}{ab}

    \frac{a^2+b^2}{ab}
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