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Math Help - Finding exact value of trigonometric expression

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    Senior Member vaironxxrd's Avatar
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    Finding exact value of trigonometric expression

    Hello Everyone,

    I'm having a little bit of trouble with the following problem.

    I need to find cos(v - u) using sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}

    I tried using those values to find the missing functions
    sin\ u = \frac{7}{25}, cos\ u = \frac{24}{25} \ and \ cos\ v = -\frac{3}{5}, sin\ v = \frac{4}{5}

    Then i used the following formula ...  cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u Replaced the numbers

    -\frac{3}{5} \cdot \frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25}
    =

    -\frac{44}{175}
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    Re: Finding exact value of trigonometric expression

    Quote Originally Posted by vaironxxrd View Post
    Hello Everyone,

    I'm having a little bit of trouble with the following problem.

    I need to find cos(v - u) using sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}

    I tried using those values to find the missing functions
    sin\ u = \frac{7}{25}, cos\ u = \frac{24}{25} \ and \ cos\ v = -\frac{3}{5}, sin\ v = \frac{4}{5}

    Then i used the following formula ...  cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u Replaced the numbers

    -\frac{3}{5} \cdot \frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25}
    =

    -\frac{44}{175}
    You can't get a unique answer unless you're told something about u and v, i.e. which quadrants they lie in...
    Thanks from vaironxxrd
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    Senior Member vaironxxrd's Avatar
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    Re: Finding exact value of trigonometric expression

    Quote Originally Posted by Prove It View Post
    You can't get a unique answer unless you're told something about u and v, i.e. which quadrants they lie in...
    Both u and v lie in Quadrant 2.

    In that case.

    sin\ u = \frac{7}{25}, \ x = -24, \ y = 7 \ r = 25 making cos\ u = -\frac{24}{25}
    cos\ v = -\frac{3}{5}. \ x = - 3, \ y = 4, \ r = 5 making sin v = \frac{4}{5}

    Then  cos(v - u) = cos\ v \cdot cos\ u + sin\ v \cdot sin\ u Replaced the numbers

    -\frac{3}{5} \cdot -\frac{24}{25} + \frac{4}{5} \cdot \frac{7}{25} = \frac{72}{125} + \frac{28}{125}
    = \frac{4}{5}
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