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- May 9th 2012, 06:31 PM #1

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## Sin Problem

- May 9th 2012, 06:33 PM #2

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- May 9th 2012, 08:28 PM #3

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- May 9th 2012, 09:53 PM #4

- May 10th 2012, 06:58 AM #5

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- May 10th 2012, 07:56 AM #6

- May 10th 2012, 08:10 AM #7

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- May 10th 2012, 08:32 AM #8
## Re: Sin Problem

$\displaystyle a\cos{x} - b\sin{x} = R\cos(x+t)$

$\displaystyle R = \sqrt{a^2+b^2}$ , $\displaystyle \tan{t} = \frac{b}{a}$

let x = your "$\displaystyle \alpha$" ...

$\displaystyle 13\cos{x} - 7\sin{x} = 9$

$\displaystyle R = \sqrt{13^2 + 7^2}$ , $\displaystyle t = \arctan\left(\frac{7}{13}\right)$

$\displaystyle R \cos(x + t) = 9$

$\displaystyle x+t = \arccos\left(\frac{9}{R}\right)$

$\displaystyle x = \arccos\left(\frac{9}{R}\right) - \arctan\left(\frac{7}{13}\right) \approx 24.14^\circ$