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Math Help - Given sinx=4/5, cosy=7/25 find the following.

  1. #1
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    Given sinx=4/5, cosy=7/25 find the following.

    Angles x and y are located in the first quadrant such that sinx=4/5, and cosy = 7/25.

    a) Determine an exact value of cosx.

    b) Determine an exact value of siny.

    c) Determine an exact value for sin(x+y)

    I'm really at a loss here, do I just sub those in to some formula or something? Can anyone help me out? Or get me pointed in the right direction? thanks in advance!!
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  2. #2
    Air
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    Quote Originally Posted by Random-Hero- View Post
    Angles x and y are located in the first quadrant such that sinx=4/5, and cosy = 7/25.

    a) Determine an exact value of cosx.
    This is a 3-4-5 triangle. If \sin x = \frac{\mathrm{Opposite}}{\mathrm{Hypotenuse}}=\fra  c{4}{5} then what is \cos x = \frac{\mathrm{Adjacent}}{\mathrm{Hypotenuse}} = ....

    Quote Originally Posted by Random-Hero- View Post
    b) Determine an exact value of siny.
    This is a 7-24-25 triangle. If \cos y = \frac{\mathrm{Adjacent}}{\mathrm{Hypotenuse}} = \frac{7}{25} then what is \sin y = \frac{\mathrm{Opposite}}{\mathrm{Hypotenuse}}= ....

    Quote Originally Posted by Random-Hero- View Post
    c) Determine an exact value for sin(x+y)

    I'm really at a loss here, do I just sub those in to some formula or something? Can anyone help me out? Or get me pointed in the right direction? thanks in advance!!
    \sin(x+y) = \sin x\cos y + \sin y \cos x thus once you have values of \sin x, \cos y, \sin y, \cos x, you can solve \sin(x+y).
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  3. #3
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    Trigonometry

    Hello Random-Hero
    Quote Originally Posted by Random-Hero- View Post
    Angles x and y are located in the first quadrant such that sinx=4/5, and cosy = 7/25.

    a) Determine an exact value of cosx.

    b) Determine an exact value of siny.

    c) Determine an exact value for sin(x+y)

    I'm really at a loss here, do I just sub those in to some formula or something? Can anyone help me out? Or get me pointed in the right direction? thanks in advance!!
    The formulae you need here are:

    \cos^2 A + \sin^2\ A = 1 and \sin(A + B) = \sin A\cos B + \cos A \sin B

    So in (a), use \cos^2 x = 1 - \sin^2x, and remember when you take the square root to find \cos x, that, since the angle x is in the first quadrant \cos x > 0, so you don't have to worry about the negative square root.

    (b) Use \sin^2y = 1 - cos^2y. And, again, since y is in the first quadrant, \sin y > 0.

    (c) simply use the formula for \sin(A+B) and your answers to (a) and (b).

    Can you complete it now?

    Grandad
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