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Math Help - cos,sin,tan

  1. #1
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    cos,sin,tan

    Given that cos A= 3/2 cosB= 24/25 where A and B are acute find the exact values of

    a) tan A

    b) sin B

    c) cos (A-B)

    d) tan(A+B)

    could any show me how these questions are solved?

    Thank you.
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Oasis1993 View Post
    Given that cos A= 3/2 cosB= 24/25 where A and B are acute find the exact values of

    a) tan A

    b) sin B

    c) cos (A-B)

    d) tan(A+B)

    could any show me how these questions are solved?

    Thank you.
    Hi oasis1993,

    The range of y=cos A is [-1, 1].

    \cos A=\frac{3}{2} is out of range.
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  3. #3
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    I dont understand how that is supposed to help me..?
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  4. #4
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    Since the given cosine equation is not possible, then there is no solution to this exercise.
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  5. #5
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    Quote Originally Posted by Oasis1993 View Post
    I dont understand how that is supposed to help me..?
    Oasis1993,

    Check to see if you copied the first cosine value correctly. Cosine A cannot be greater than 1 or less than -1. You have it as 3/2, which is greater than 1.
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  6. #6
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    The question says 3/5.
    I know we are supposed to use the identities and addition formulae's...but i dont really know how.
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  7. #7
    A riddle wrapped in an enigma
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    Quote Originally Posted by Oasis1993 View Post
    Given that cos A= 3/5 cosB= 24/25 where A and B are acute find the exact values of

    a) tan A

    b) sin B

    c) cos (A-B)

    d) tan(A+B)

    could any show me how these questions are solved?

    Thank you.
    Quote Originally Posted by Oasis1993 View Post
    The question says 3/5.
    I know we are supposed to use the identities and addition formulae's...but i dont really know how.
    Ok, Oasis1993, that helps.

    Since Cos A = 3/5, this means that x = 3 and r = 5. Solve for y in the following equation:

    r^2=x^2+y^2

    (a) \tan A = \frac{y}{x}

    Since Cos B = 24/25, this means that x = 24 and r = 25. Solve for y in the following equation:

    r^2=x^2+y^2

    (b) \sin B = \frac{y}{r}

    For (c) and (d), use your sum-difference formulas using the information you are given and the information you found.
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