Find the value of $csc(frac{pi}{3})$ using the unit circle

To find $\csc(\frac{\pi}{3})$, we first need to recall the definition of the cosecant function:

$\csc(\theta) = \frac{1}{\sin(\theta)}$

Next, we locate the angle $\frac{\pi}{3}$ on the unit circle. The sine of $\frac{\pi}{3}$ is given by:

$\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$

Now, using the definition of cosecant:

$\csc(\frac{\pi}{3}) = \frac{1}{\sin(\frac{\pi}{3})} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}$

Therefore, $\csc(\frac{\pi}{3}) = \frac{2\sqrt{3}}{3}$.

To find $csc(frac{pi}{3})$, we use the definition of cosecant:

$csc( heta) = frac{1}{sin( heta)}$

The angle $frac{pi}{3}$ on the unit circle has a sine value of:

$sin(frac{pi}{3}) = frac{sqrt{3}}{2}$

Thus,

$csc(frac{pi}{3}) = frac{1}{sin(frac{pi}{3})} = frac{1}{frac{sqrt{3}}{2}} = frac{2}{sqrt{3}}$

Simplifying, we get:

$csc(frac{pi}{3}) = frac{2sqrt{3}}{3}$

Therefore, $csc(frac{pi}{3}) = frac{2sqrt{3}}{3}$.

Let’s find $csc(frac{pi}{3})$:

$csc(frac{pi}{3}) = frac{1}{sin(frac{pi}{3})}$

Since $sin(frac{pi}{3}) = frac{sqrt{3}}{2}$, we have

$csc(frac{pi}{3}) = frac{2}{sqrt{3}} = frac{2sqrt{3}}{3}$

Therefore, $csc(frac{pi}{3}) = frac{2sqrt{3}}{3}$.

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