Find the exact value of the expression \( \tan \left(\cos ^{-1}\left(-\frac{1}{2}\right)\right) \) \[ \boldsymbol{\operatorname { t a n }}\left(\boldsymbol{\operatorname { c o s }}^{-1}\left(-\frac{1}{2}\right)\right)=\square \] (Type an exact answer, using \( \pi \) and radicals as needed.)
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We need to find this angle in the unit circle where the cosine value is negative. Cosine is negative in the second and third quadrants of the unit circle. However, the range of the inverse cosine function is \(0\) to \(\pi\), which means we are looking for an Show moreā¦
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