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Find the exact value of each expression, if it exists. cos1(32)\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)


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We find a point on the unit circle on the interval [0,π][0,\pi] with a xx-coordinate of 32-\dfrac{\sqrt{3}}{2}. When t=5π6t=\dfrac{5\pi}{6}, cost=32\cos{t}=-\dfrac{\sqrt{3}}{2}. Therefore, cos1(32)=5π6\cos^{-1}{(-\dfrac{\sqrt{3}}{2})}=\dfrac{5\pi}{6}.

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