Question

Find the exact value by using a half-angle identity.
cos(5π/12)

I know someone knows how to do this! if you could explain too, that'd be great!

Answer 1

\(\bf cos\left(\frac{5\pi}{12}\right)\\ \quad \\ \quad \\
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\cfrac{5}{12}\times 2\implies \cfrac{5}{6}\\ \quad \\
cos\left(\frac{5\pi}{12}\right)\implies cos\left(\cfrac{\frac{5\pi}{6}}{2}\right)\\ \quad \\
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cos\left(\frac{\theta}{2}\right) = \pm \sqrt{\cfrac{1+cos(\theta)}{2}}\\ \quad \\
cos\left(\cfrac{\frac{5\pi}{6}}{2}\right) = \pm \sqrt{\cfrac{1+cos\left(\frac{5\pi}{6}\right)}{2}}
\)

now, check your Unit Circle to see what's the \(\bf cos\left(\frac{5\pi}{6}\right)\)