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Math Help - trigonometric identities

  1. #1
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    trigonometric identities

    I am trying to learn how to transform identities of one side of the equation to the other side. is this correct?


    I am using 0 for theta
    theta = 0

    question:

    tan 0 + cot 0
    -------------- = csc^2 0

    tan 0


    answer:

    cot 0 = csc 0

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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by robasc View Post
    I am trying to learn how to transform identities of one side of the equation to the other side. is this correct?


    I am using 0 for theta
    theta = 0

    question:

    tan 0 + cot 0
    -------------- = csc^2 0

    tan 0


    answer:

    cot 0 = csc 0

    that answer is wrong. how does that prove an identity. you must show the left hand side and right hand side are the same. so you must turn one side into the other or bring both sides to the same thing

    consider the left hand side (it is more complicated and so gives us more options to change things)

    note, \frac {\tan \theta + \cot \theta}{\tan \theta} = \frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta}

    now what?
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  3. #3
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    On the left side I know that I will be left with tan 0.

    but the right side confuses me.

    wait I think I got it:

    tan 0 = sin 0 / cos 0
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by robasc View Post
    On the left side I know that I will be left with tan 0.

    but the right side confuses me.

    wait I think I got it:

    tan 0 = sin 0 / cos 0
    yes, it you can use that

    now how do we finish the problem?
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  5. #5
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    so the answer is tan 0?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by robasc View Post
    so the answer is tan 0?
    huh??

    lets not lose sight of the objective here. we are proving an identity. we are trying to turn one side into the other. your objective is to turn \frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta} into \csc^2 \theta through simplification. that will show that the left hand side and right hand side are the same
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  7. #7
    Super Member 11rdc11's Avatar
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    I'm going to work this out for you since it seems you are a little lost and hopefully me working it will help you understand, but I what you to come back and explain the steps I did so you will learn.

    \frac {\tan \theta + \cot \theta}{\tan \theta}

    =~\frac {\tan \theta}{\tan \theta} + \frac {\cot \theta}{\tan \theta}

    = 1+ \frac{cos^2\theta}{sin^2\theta}

    = \frac{sin^2\theta}{sin^2\theta} + \frac{cos^2\theta}{sin^2\theta}

    =~\frac{1}{sin^2\theta}

    =~csc^2\theta
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  8. #8
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    ok I have come up with this:

    sin/cos + cos/sin
    ------------------
    sin/cos + sin/cos

    cos/sin
    -------
    sin/cos


    cos/sin * cos/sin =

    cos^2 0
    --------
    sin^2 0



    this is how I am thinking about it?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by robasc View Post
    ok I have come up with this:

    sin/cos + cos/sin
    ------------------
    sin/cos + sin/cos
    evidently you need help with adding fractions (see posts #3, 9 and 11 here). you cannot cancel like that! and you cannot have sin and cos by themselves, write sin(x) and cos(x) or something

    furthermore, as i said, you are proving an identity. if you don't end up with something that looks like the other side, you are wrong

    this is how I am thinking about it?
    you're asking us or telling us?

    11rdc11 did the problem for you. make sure you follow what he did
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  10. #10
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    I was telling you how I was interpreting the problem.
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  11. #11
    Super Member 11rdc11's Avatar
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    Oops I didn't notice that help canceled out \frac{sin\theta}{cos\theta} like that
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  12. #12
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by robasc View Post
    I was telling you how I was interpreting the problem.
    yes, i know. i was messing with you because you put a question mark at the end.

    study what 11rdc11 did and make sure you have no questions. then, make sure you review fractions and trig identities. things like \sin^2 \theta + \cos^2 \theta = 1, stuff like that you should know by heart. you are in for a LOT of pain if you do not get these basic things. you don't want to be one of those students that end up in calculus and can't do basic algebra, trust me
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