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anonymous
 5 years ago
cos(3π/8) Without a calculator. has to be exact…
anonymous
 5 years ago
cos(3π/8) Without a calculator. has to be exact…

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watchmath
 5 years ago
Best ResponseYou've already chosen the best response.0First we need to know \(\cos(\pi/8)\). Let \(x=\pi/8\). \(\cos(2x)=2\cos^2(x)1\) On the other hand \(\cos(2x)=\cos(\pi/4)=\frac{1}{2}\sqrt{2}\) It follows that \(2\cos^2(x)1=\frac{1}{2}\sqrt{2}\) \(\cos x=\frac{1}{2}\sqrt{1+\frac{1}{2}\sqrt{2}}\). Then compute \(cos(3\pi/8)\) by using \(\cos(3\pi/8)=\cos((\pi/8)+(\pi/4))=\cos(\pi/8)\cos(\pi/4)\sin(\pi/8)\sin(\pi/4)\).
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