What are the sine, cosine, and tangent of the angle $frac{pi}{3}$ on the unit circle?

First, locate the angle $\frac{\pi}{3}$ on the unit circle. This angle corresponds to 60 degrees.

The coordinates of the point on the unit circle at this angle are $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$.

Thus, the cosine of $\frac{\pi}{3}$ is the x-coordinate, which is $\frac{1}{2}$:

$\cos \frac{\pi}{3} = \frac{1}{2}$

The sine of $\frac{\pi}{3}$ is the y-coordinate, which is $\frac{\sqrt{3}}{2}$:

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

The tangent is given by the ratio of the sine to the cosine:

$\tan \frac{\pi}{3} = \frac{\sin \frac{\pi}{3}}{\cos \frac{\pi}{3}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \sqrt{3}$

To find the sine, cosine, and tangent of $frac{pi}{3}$ on the unit circle, recognize the angle as 60 degrees.

The unit circle coordinates for $frac{pi}{3}$ are $left(frac{1}{2}, frac{sqrt{3}}{2}
ight)$.

The cosine, which is the x coordinate, is:

$cos frac{pi}{3} = frac{1}{2}$

The sine, which is the y coordinate, is:

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

The tangent, the ratio of sine to cosine, is:

$ an frac{pi}{3} = frac{frac{sqrt{3}}{2}}{frac{1}{2}} = sqrt{3}$

For angle $frac{pi}{3}$ (60 degrees) on unit circle:

Cosine: $cos frac{pi}{3} = frac{1}{2}$

Sine: $sin frac{pi}{3} = frac{sqrt{3}}{2}$

Tangent: $ an frac{pi}{3} = sqrt{3}$

Start Using PopAi Today