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Thread: 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 $\displaystyle cos(v - u)$ using $\displaystyle sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}$

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

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

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

    $\displaystyle -\frac{44}{175}$
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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 $\displaystyle cos(v - u)$ using $\displaystyle sin\ u = \frac{7}{25}, cos\ v = -\frac{3}{5}$

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

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

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

    $\displaystyle -\frac{44}{175}$
    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.

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

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

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