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Evaluate. Write your answer in simplified, rationalized form. Do not round. $\newline$ $\csc 60^\circ =$ ______

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Csc, sec, and cot of special angles

Full solution

Q. Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

______

Find $\sin 60°$ : To find the value of $\csc 60°$ , we first need to find the value of $\sin 60°$ and then take its reciprocal, since $\csc \theta = \frac{1}{\sin \theta}$ .
Calculate $\csc 60°$ : The value of $\sin 60°$ is known to be $\sqrt{3}/2$ . Therefore, $\csc 60° = 1/(\sin 60°) = 1/(\sqrt{3}/2)$ .
Simplify $\frac{1}{\sqrt{3}/2}$ : To simplify $\frac{1}{\sqrt{3}/2}$ , we multiply both the numerator and the denominator by $2$ to get rid of the fraction in the denominator. This gives us $\frac{2}{\sqrt{3}}$ .
Rationalize the denominator: To rationalize the denominator of $\frac{2}{\sqrt{3}}$ , we multiply both the numerator and the denominator by $\sqrt{3}$ to get $\frac{2 \sqrt{3}}{3}$ .

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