Determine the Values of Trigonometric Functions at $frac{pi}{3}$

Consider the angle $\frac{\pi}{3}$ on the unit circle. To find the values of sin, cos, and tan at this angle, we use the known values:

The sine of $\frac{\pi}{3}$ is:

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

The cosine of $\frac{\pi}{3}$ is:

$\cos \left( \frac{\pi}{3} \right) = \frac{1}{2}$

Using the quotient identity for tangent:

$\tan \left( \frac{\pi}{3} \right) = \frac{\sin \left( \frac{\pi}{3} \right)}{\cos \left( \frac{\pi}{3} \right)} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

Given the angle $frac{pi}{3}$, let’s determine the trigonometric function values:

First, we find:

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

Next, for cosine:

$cos left( frac{pi}{3}
ight) = frac{1}{2}$

Finally, the tangent function value:

$ an left( frac{pi}{3}
ight) = frac{sqrt{3}}{2} div frac{1}{2} = sqrt{3}$

For $frac{pi}{3}$:

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

$cos left( frac{pi}{3}
ight) = frac{1}{2}$

$ an left( frac{pi}{3}
ight) = sqrt{3}$

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