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Algebra applied to Trigonometry problem

  1. Jan 19, 2010 #1
    1. The problem statement, all variables and given/known data

    tansquaredB=4

    solving for B

    2. Relevant equations
    This is algebra applied to Trigonometry, through simplification, to arrive at several different answers involving the degrees of angles.

    I hope this applies to Physics since physics is "applied Mathematics"


    3. The attempt at a solution

    B=-tansquared+4

    I don't know how to arrive at degrees.
     
  2. jcsd
  3. Jan 19, 2010 #2

    Mark44

    Staff: Mentor

    Re: Trigonometry

    With all due respect, your attempt is completely wrong. You are treating "tansquared" is if it had been added on the left side, and have subtracted it from both sides.

    Your original equation has nothing to do with addition or subtraction. It is (tan(B))2 = 4. It probably appears in your text as tan2B = 4, which is the same as what I wrote earlier.

    Your equation is saying that a certain quantity (tan(B)) squared equals 4. What can you do to get rid of the exponent?
     
  4. Jan 20, 2010 #3

    Mentallic

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    Homework Helper

    Re: Trigonometry

    Trigonometry definitely applies to physics. You'll be using it all the time in projectile problems and some other topics.

    I recommend you study some trigonometry from a maths textbook.
     
  5. Jan 23, 2010 #4
    Re: Trigonometry

    There are 2 answers...
     
  6. Jan 24, 2010 #5

    Mentallic

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    Re: Trigonometry

    You'd need to be more specific. There are two equations to solve, essentially [itex]tan(B)=\pm 2[/itex] but there are infinite solutions for B.
    But the context of this question is for physics, so there will of course be a restriction on the values of B.
     
  7. Jan 24, 2010 #6
    Re: Trigonometry

    This is a homework help forum ... I don't want to get too specific.

    Unless you consider [tex]n^\circ[/tex] and [tex](n+360)^\circ[/tex] to be different angles (which they are not) then there are only 2 answers.

    Angles measured in degrees should be represented by the values: [itex]0 \le n < 360[/tex]
    Angles measured in radians should be represented by the values: [itex]0 \le n < 2\pi[/tex]
    Angles measured in gradians should be represented by the values [itex]0 \le n < 400[/tex]
     
  8. Jan 25, 2010 #7

    Mentallic

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    Re: Trigonometry

    Physically, yes, but in most mathematics such angles are considered as different solutions. This is why most trigonometry questions are coupled with restrictions as such: (but it is important to be aware that such questions typically have infinite solutions).

    That's fine, but this doesn't support your - still - incorrect statement:
    With these restrictions, there are 4 answers.
     
  9. Jan 25, 2010 #8
    Re: Trigonometry

    Yes, you are right ... there are 4 answers!
     
  10. Jan 25, 2010 #9

    Mentallic

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    Re: Trigonometry

    :tongue:
     
  11. Jan 26, 2010 #10
    Re: Trigonometry

    Normally I would factor anything with an exponent, to get rid of it.

    The problem calls for degrees.

    Are 63.43 and 116.57 degrees acceptable solutions?

    Thanks!
     
  12. Jan 26, 2010 #11
    Re: Trigonometry

    That's 2 out of 4!!!!
     
  13. Jan 26, 2010 #12

    Mentallic

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    Re: Trigonometry

    It depends what the question is asking for. You need to solve [itex]tanB=2[/itex] and [itex]tanB=-2[/itex] so you'd be correct with those solutions, but there are more answers because [itex]tan\theta=tan(\theta+n180^o[/itex] so you could also have 243.43o and 423.43o and this goes on infinitely. Is the restriction on the domain [itex]0\leq B < 360^o[/itex] or something similar?
     
  14. Jan 27, 2010 #13
    Re: Trigonometry

    Yes that is the domain like you said.
     
  15. Jan 27, 2010 #14
    Re: Trigonometry

    Like I said, there are 4 answers, and you already got 2 of them:

    [tex]63.43^\circ [/tex] and [tex]116.57^\circ[/tex]


    The other 2 would be:

    [tex]-63.43^\circ = 296.57^\circ[/tex] and [tex]-116.57^\circ = 243.43^\circ[/tex]
     
  16. Jan 28, 2010 #15
    Re: Trigonometry

    Thank You both Very Much!
     
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