Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator.
$\frac{5 π}{3}$

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Final Answer: $\sin (\frac{5 π}{3}) = \frac{\sqrt{3}}{2}, \cos (\frac{5 π}{3}) = \frac{1}{2}, \tan (\frac{5 π}{3}) = \sqrt{3}$ , $\csc (\frac{5 π}{3}) = \frac{2}{\sqrt{3}}, \sec (\frac{5 π}{3}) = 2, \cot (\frac{5 π}{3}) = \frac{1}{\sqrt{3}}$

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Step 1 ：The angle $\frac{5 π}{3}$ is in standard position and it is a positive angle measured counterclockwise from the positive x-axis. The angle $\frac{5 π}{3}$ is equivalent to $\frac{π}{3}$ because $5 π / 3 = 2 π + π / 3$ , and $2 π$ is a full rotation which brings us back to the same position.

Step 2 ：The six trigonometric functions of $\frac{π}{3}$ are well known. They are: $\sin (\frac{π}{3}) = \frac{\sqrt{3}}{2}$ , $\cos (\frac{π}{3}) = \frac{1}{2}$ , $\tan (\frac{π}{3}) = \sqrt{3}$ , $\csc (\frac{π}{3}) = \frac{2}{\sqrt{3}}$ , $\sec (\frac{π}{3}) = 2$ , $\cot (\frac{π}{3}) = \frac{1}{\sqrt{3}}$

Step 3 ：So, the six trigonometric functions of $\frac{5 π}{3}$ are the same as those of $\frac{π}{3}$ .

Step 4 ：Final Answer: $\sin (\frac{5 π}{3}) = \frac{\sqrt{3}}{2}, \cos (\frac{5 π}{3}) = \frac{1}{2}, \tan (\frac{5 π}{3}) = \sqrt{3}$ , $\csc (\frac{5 π}{3}) = \frac{2}{\sqrt{3}}, \sec (\frac{5 π}{3}) = 2, \cot (\frac{5 π}{3}) = \frac{1}{\sqrt{3}}$

Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator.5π3

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Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator.
$\frac{5 π}{3}$