Determine arccos(sin 49*pi /8)

The answer can be written in the form a/b where a/b is an abbreviated fraction.

a =?

b =?

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- Oct 2nd 2009, 03:56 AMsf1903Trigonometric functions, arcus functions
Determine arccos(sin 49*pi /8)

The answer can be written in the form a/b where a/b is an abbreviated fraction.

a =?

b =? - Oct 2nd 2009, 04:48 AMAmer

$\displaystyle \sin A = \cos (\frac{\pi}{2} - A) $ and

$\displaystyle \sin (2\pi+A) =\sin A $

$\displaystyle \cos ^{-1} (\cos A) = A $

ok

$\displaystyle \cos ^{-1} (\sin \frac{49\pi}{8})$ but

$\displaystyle \frac{49\pi}{8} = 6\pi + \frac{\pi}{8} = 3(2\pi) + \frac{\pi}{8} $

so

$\displaystyle \cos ^{-1} ( \sin \frac{\pi}{8})$

$\displaystyle \cos ^{-1} (\cos (\frac{\pi}{2} - \frac{\pi}{8}))=\frac{\pi}{2} - \frac{\pi}{8}$