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Thread: Trig

  1. #1
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    Trig

    Hey.

    1- Express 12cosx+ 9sinx in the form Rcos(x-A) where R is greater than 0 and A is between 0 and 90.

    I did this one and got 15cos(x-0,644) (in radians)

    I cant do the second part.

    b) Use the method of part a to find the smallest positve root of A of the equation 12cosx+9sinx = 14

    Thanks.
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  2. #2
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    Hello Oasis1993
    Quote Originally Posted by Oasis1993 View Post
    Hey.

    1- Express 12cosx+ 9sinx in the form Rcos(x-A) where R is greater than 0 and A is between 0 and 90.

    I did this one and got 15cos(x-0,644) (in radians)

    I cant do the second part.

    b) Use the method of part a to find the smallest positve root of A of the equation 12cosx+9sinx = 14

    Thanks.
    You're right so far!

    For part (b), just say:
    $\displaystyle 15\cos(x-A) = 14$

    $\displaystyle \Rightarrow \cos(x-A)=\frac{14}{15}= 0.9333$

    $\displaystyle \Rightarrow x-A = \pm 0.3672 +2n\pi, n \in \mathbb{Z}$ (Do you understand this bit?)

    $\displaystyle \Rightarrow x = A \pm 0.3672 + 2n\pi$
    And for the smallest positive value of $\displaystyle x$, which sign do we take, and which value of $\displaystyle n$? (I get the answer $\displaystyle x=0.277$. Do you?)

    Grandad
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  3. #3
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    Thank you!

    Yes your answer is correct.
    But i didnt understand that part where you asked...?
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  4. #4
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    Hello Oasis1993
    Quote Originally Posted by Oasis1993 View Post
    Thank you!

    Yes your answer is correct.
    But i didnt understand that part where you asked...?
    The principal value of $\displaystyle (x - A)$ is $\displaystyle 0.3672$ radians. Other angles that will have the same cosine as this will be $\displaystyle 0.3672$ radians on either side of a multiple of $\displaystyle 2\pi$. Any multiple of $\displaystyle 2\pi$ is $\displaystyle 2n\pi$, and 'on either side' of this means adding or subtracting $\displaystyle 0.3672$ from $\displaystyle 2n\pi$. Hence $\displaystyle \pm0.3672 + 2n\pi$.

    Grandad
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