# Find the exact value of \cot(\arcsin\frac{3}{8}) without using a calculato

Find the exact value of $$\displaystyle{\cot{{\left({\arcsin{{\frac{{{3}}}{{{8}}}}}}\right)}}}$$ without using a calculator.

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1.$$\displaystyle{a}{d}{j}=\sqrt{{{h}{y}{p}^{{{2}}}-{o}{p}{p}^{{{2}}}}}=\sqrt{{{8}^{{{2}}}-{3}^{{{2}}}}}=\sqrt{{{55}}}$$
2. $$\displaystyle{\cot{\theta}}={\frac{{{a}{d}{j}}}{{{o}{p}{p}}}}={\frac{{\sqrt{{55}}}}{{{3}}}}$$
Result :$$\displaystyle{\frac{{\sqrt{{55}}}}{{{3}}}}$$