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Math Help - Find the exact values.

  1. #1
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    Find the exact values.

    Let sin x = -3/5, where 3π/2x , and cos y = -5/13, where π ≤ x ≤ 3π/2. Find the exact value of

    a) cos2x

    b) cos(y/2)

    c) cos(x + y)

    d) sin (x - y)

    My work:

    a) cos2x = 1 - 2sin^2x

    for sin x = -3/5 -----> 1-2(-3/5)^2 = 7/25

    for cosy = -5/13 -----> 1-2(-12/13)^2 = -119/169

    b) cos(y/2) =
    √(1+ cosy)/2

    for cosy = -5/3 -----> √(1+(-5/13))/2 = 2/√13

    for siny = -3/5 -----> √(1+(4/5))/2 = 3/(2√5)

    c) cos(x + y) = (cosx)(cosy) - (sinx)(siny)

    (4/5)(-5/13) - (-3/5)(-12/13)

    (-20/65) - (36/65) = -56/65

    d) sin(x - y) = (sinx)(cosy) + (cosx)(siny)

    (-3/5)(-5/13) + (4/5)(-12/13)

    = (-15/65) + (-48/65) = -63/65


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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Find the exact values.

    Quote Originally Posted by FatimaA View Post
    My work:

    a) cos2x = 1 - 2sin^2x

    for sin x = -3/5 -----> 1-2(-3/5)^2 = 7/25
    Right

    Quote Originally Posted by FatimaA View Post
    for cosy = -5/13 -----> 1-2(-12/13)^2 = -119/169
    You have found the value for cos(2y), but that wasn't asked for.

    Quote Originally Posted by FatimaA View Post
    b) cos(y/2) = √(1+ cosy)/2

    for cosy = -5/3 -----> √(1+(-5/13))/2 = 2/√13
    Good.

    Quote Originally Posted by FatimaA View Post
    for siny = -3/5 -----> √(1+(4/5))/2 = 3/(2√5)
    Looks like you're trying to find the value of cos(x/2), which wasn't asked for. If so, the 2 belongs inside the square root sign, so it should be 3/sqrt(10)

    Quote Originally Posted by FatimaA View Post
    c) cos(x + y) = (cosx)(cosy) - (sinx)(siny)

    (4/5)(-5/13) - (-3/5)(-12/13)

    (-20/65) - (36/65) = -56/65
    You have siny = -12/13, but are you sure it isn't actually +12/13? Your post is a bit garbled regarding what quadrant y is in, so I can't really tell whether this is correct or not.


    Quote Originally Posted by FatimaA View Post
    d) sin(x - y) = (sinx)(cosy) + (cosx)(siny)
    No, sin(x-y) = sinx cosy - cos x siny
    Last edited by ebaines; June 13th 2013 at 11:32 AM.
    Thanks from topsquark and FatimaA
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  3. #3
    MHF Contributor

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    Re: Find the exact values.

    You understand, do you not, that your " 3\pi/2= x= 2\pi" and " \pi= y= 3\pi/2" are nonsense? x cannot be equal to two different numbers (and neither 3\pi/2 nor 2\pi has sine equal to -3/5). I think you meant 3\pi/2\le x\le 2\pi and \pi\le y\le 3\pi/2. That is that x is in the fourth quadrant and y is in the third quadrant.
    Thanks from FatimaA and topsquark
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