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timurjin [86]
3 years ago
11

Find the exact value of cos(7\pi /12)

Mathematics
1 answer:
Naya [18.7K]3 years ago
7 0

7π/12 lies in the second quadrant, so we expect cos(7π/12) to be negative.

Recall that

\cos^2x=\dfrac{1+\cos(2x)}2

which tells us

\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1+\cos\left(\frac{7\pi}6\right)}2}

Now,

\cos\left(\dfrac{7\pi}6\right)=-\cos\left(\dfrac\pi6\right)=-\dfrac{\sqrt3}2

and so

\cos\left(\dfrac{7\pi}{12}\right)=-\sqrt{\dfrac{1-\frac{\sqrt3}2}2}=\boxed{-\dfrac{\sqrt{2-\sqrt3}}2}

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