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Thread: Use trig idents to simplify tan(-β)cos(β)= -tan(β) cos(β)= -sinβ/cosβ * cosβ/1=...

  1. #1

    Use trig idents to simplify tan(-β)cos(β)= -tan(β) cos(β)= -sinβ/cosβ * cosβ/1=...

    Use trigonomeric identities to simplify the expression.

    tan(-β)cos(β)=

    -tan(
    β) cos(β)= -sinβ/cosβ * cosβ/1= -sinβ

    my teacher worked this out, but I still don't understand, what formula was used to solve this?

  2. #2
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    Please show YOUR work.

    Rule of Thumb: When in doubt, change everything to sines and cosines.

    See if that gets you anywhere.

    Note: The REAL trick to these things is to TRY SOMETHING. Don't sit and stare at it. Do ANYTHING. Trust me on this. It's just an equation. You can't break it. You might learn things by working through things that don't get you anywhere.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Quote Originally Posted by melmath View Post
    Use trigonomeric identities to simplify the expression.

    tan(-β)cos(β)=

    -tan(
    β) cos(β)= -sinβ/cosβ * cosβ/1= -sinβ

    my teacher worked this out, but I still don't understand, what formula was used to solve this?
    The first step here is to change [tex]tan(-\beta)[/tex] to [tex]-tan(\beta)[/tex]. This should be an identity you would have learned, which says that tan is an odd function.

    The second step is to express everything in terms of sine and cosine; that is, to replace [tex]tan(\beta)[/tex] with [tex]\dfrac{sin(\beta)}{cos(\beta)}[/tex]. This is called the quotient identity.

    The third step is just algebra, multiplying two fractions.

    If you have a list of identities, recognizing what your teacher did is just a matter of pattern matching: look for an identity that looks like what is being done. If you have trouble doing that, focus on what is changing from one step to the next.

    If you don't have a list of identities, make one! Take all the identities you have learned and put them on one sheet of paper so you can see them all at once.

    Reading work like this is an important skill, which comes before writing (that is, doing the simplification yourself). So you will want to look at examples in your textbook or online sites until you can follow what is being done.

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    Quote Originally Posted by Dr.Peterson View Post
    If you don't have a list of identities, make one! Take all the identities you have learned and put them on one sheet of paper so you can see them all at once.
    Can't argue with that. I remember my first trig book had "Page 89". It was jam packed full of identities. It was a very worn out page.
    "Unique Answers Don't Care How You Find Them." - Many may have said it, but I hear it most from me.

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    Quote Originally Posted by tkhunny View Post
    Note: The REAL trick to these things is to TRY SOMETHING. Don't sit and stare at it. Do ANYTHING. Trust me on this. It's just an equation. You can't break it. You might learn things by working through things that don't get you anywhere.
    This is excellent advice; I've been saying the same thing in the last couple weeks to many students, whom I help face to face in a college tutoring center. I described this kind of work as finding your way in a fog -- you may not see what to do yet, but each step you take will make something new visible, giving you a new possibility. Sometimes there is nothing you can do until you take that first step.

    When you read someone else's work, you are tailgating behind them in the fog, in order to see where they are going. You should also be looking around occasionally to see what they might be seeing that leads them to make the choices they make. In this case, your teacher probably saw first that the functions didn't all have the same argument (some had [tex]\beta[/tex], others had [tex]-\beta[/tex]), so changing that was a top priority. Then he saw that there was a mix of different functions, so putting them all in terms of sine and cosine would simplify the tangle. Then things sort of fell into place.

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