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Math Help - trigo equation

  1. #1
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    Post trigo equation

    find, for 0=<A=<360
    (A:tan^(3A)=tanA)
    i stuck at tan^3 and tanA.

    find 6tan^2(A)-4sin^2(A)=1 , 0=<A=<360
    i stuck at 6tan^2(A).
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  2. #2
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    Quote Originally Posted by sanikui View Post
    find, for 0=<A=<360
    (A:tan^(3A)=tanA)

    i stuck at tan^3 and tanA.

    [snip]
    \tan^3 A - \tan A = 0 \Rightarrow \tan A (\tan^2 A - 1) = 0.

    Case 1: \tan A = 0.

    Case 2: \tan^2 A - 1 = 0 \Rightarrow \tan^2 A = 1 \Rightarrow \tan A = \pm 1.

    Case 2 (a): \tan A = 1.

    Case 2 (b): \tan A = -1.

    Solve each case over the given domain.
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  3. #3
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    Quote Originally Posted by sanikui View Post
    [snip]
    find 6tan^2(A)-4sin^2(A)=1 , 0=<A=<360
    i stuck at 6tan^2(A).
    One possible approach (there are many others):

    Substitute \tan^2 A = \frac{1}{\cos^2 A} - 1 and \sin^2 A = 1 - \cos^2 A.

    Re-arrange and simplify: 2 \cos^4 A - 5 \cos^2 A + 3 = 0 \Rightarrow (\cos A - 1)(2 \cos A - 3) = 0.

    Therefore you need to solve \cos A = 1 over the given domain (the other case has no real solutions - why?)
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  4. #4
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    question 1, i know do liaw....thx ~!
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  5. #5
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    O.o
    For question 2, i know the answer A is 30*, 150*, 210*, 330*.
    But the problem is didnt how to do.

    Thx for helping~!V^^
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    One possible approach (there are many others):

    Substitute \tan^2 A = \frac{1}{\cos^2 A} - 1 and \sin^2 A = 1 - \cos^2 A.

    Re-arrange and simplify: 2 \cos^4 A - 5 \cos^2 A + 3 = 0 \Rightarrow (\cos A - 1)(2 \cos A - 3) = 0.

    Therefore you need to solve \cos A = 1 over the given domain (the other case has no real solutions - why?)
    I made several careless errors. Here is the corrected reply:

    Re-arrange and simplify: 4 \cos^4 A - 11 \cos^2 A + 6 = 0 \Rightarrow (\cos^2 A - 2)(4 \cos^2 A - 3) = 0.

    Therefore you need to solve \cos^2 A = \frac{3}{4} \Rightarrow \cos A = \pm \frac{\sqrt{3}}{2} over the given domain (the other case has no real solutions - why?)
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  7. #7
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    cos^2(A)=3/4 this undefined.
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  8. #8
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    Quote Originally Posted by sanikui View Post
    cos^2(A)=3/4 this undefined.
    No. It IS defined.
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