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Thread: Trigonometry

  1. #1
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    Trigonometry

    If $\displaystyle sin\;\beta = \frac{2}{7}$ find $\displaystyle cos\;2\beta$ without using a calculator.

    First off I know that $\displaystyle cos\;2\beta = 1 - 2\;sin^2\;\beta$

    But I'm having trouble plugging in the $\displaystyle sin\;\beta = \frac{2}{7}$

    Anyone have any thoughts on this?
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  2. #2
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    Quote Originally Posted by OzzMan View Post
    If $\displaystyle sin\;\beta = \frac{2}{7}$ find $\displaystyle cos\;2\beta$ without using a calculator.

    First off I know that $\displaystyle cos\;2\beta = 1 - 2\;sin^2\;\beta$

    But I'm having trouble plugging in the $\displaystyle sin\;\beta = \frac{2}{7}$

    Anyone have any thoughts on this?
    Why not $\displaystyle cos\;2\beta = 1 - 2\;sin^2\;\beta = 1 - 2 \left( \frac{2}{7}\right)^2$ .....?

    Hmmmmmm ...... you do realise that $\displaystyle \sin^2 \beta$ means $\displaystyle (\sin \beta)^2$, right ....?
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  3. #3
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    $\displaystyle
    cos\;2\beta = 1 - 2\;sin^2\;\beta
    $

    Remember that:

    $\displaystyle sin^2\;\beta = (sin \beta)^2$

    So simply plug in $\displaystyle \frac {2}{7}$ :

    $\displaystyle cos\;2\beta = 1 - 2 \left( \frac{2}{7}\right)^2$
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  4. #4
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    I thought you had to leave a sin in there because it was $\displaystyle sin = \frac{2}{7}$ not $\displaystyle sin^2 = \frac{2}{7}$

    Alright so the answers $\displaystyle cos\;2\beta = \frac{41}{49}$
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  5. #5
    Senior Member topher0805's Avatar
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    Quote Originally Posted by OzzMan View Post
    I thought you had to leave a sin in there because it was $\displaystyle sin = \frac{2}{7}$ not $\displaystyle sin^2 = \frac{2}{7}$
    You are right, it was $\displaystyle sin = \frac{2}{7}$ not $\displaystyle sin^2 = \frac{2}{7}$ .

    That is why you have to square the $\displaystyle \frac {2}{7}$ .

    Quote Originally Posted by OzzMan View Post
    Alright so the answers $\displaystyle cos\;2\beta = \frac{41}{49}$
    Yes but it should be negative.
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  6. #6
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    $\displaystyle 1 - 2\left(\frac{2}{7}\right)^2$

    $\displaystyle 1 - 2\left(\frac{4}{49}\right)$

    $\displaystyle 1 - \frac{8}{49}$

    $\displaystyle \frac{49}{49} - \frac{8}{49}$

    $\displaystyle \frac{41}{49}$
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  7. #7
    Senior Member topher0805's Avatar
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    Oops, sorry you are right.
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