Find the coordinates of the point on the unit circle at an angle of $240^circ$.

First, we convert 240 degrees to radians since the unit circle is often used with radians. The conversion factor is $\pi$ radians = 180 degrees.

Thus, $240^\circ = \frac{240 \cdot \pi}{180} = \frac{4\pi}{3} \text{ radians}$

Next, we find the coordinates of the point on the unit circle at an angle of $\frac{4\pi}{3}$ radians. By using the $\cos$ and $\sin$ functions:

$x = \cos\left(\frac{4\pi}{3}\right)$

$y = \sin\left(\frac{4\pi}{3}\right)$

Since $\frac{4\pi}{3}$ is in the third quadrant, where both cosine and sine are negative:

$\cos\left(\frac{4\pi}{3}\right) = -\frac{1}{2}$

$\sin\left(\frac{4\pi}{3}\right) = -\frac{\sqrt{3}}{2}$

Therefore, the coordinates are:

$\boxed{\left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)}$

To find the coordinates of the point on the unit circle at an angle of $240^circ$, we start by noting that 240 degrees places the point in the third quadrant.

The reference angle is:

$240^circ – 180^circ = 60^circ$

The cosine and sine values for 60 degrees are:

$cos(60^circ) = frac{1}{2}$

$sin(60^circ) = frac{sqrt{3}}{2}$

Because we are in the third quadrant, both the cosine and sine values will be negative:

$cos(240^circ) = -frac{1}{2}$

$sin(240^circ) = -frac{sqrt{3}}{2}$

Thus, the coordinates are:

$oxed{left(-frac{1}{2}, -frac{sqrt{3}}{2}
ight)}$

For an angle of $240^circ$, determine the reference angle:

$240^circ – 180^circ = 60^circ$

Third quadrant values are negative:

$cos(240^circ) = -frac{1}{2}$

$sin(240^circ) = -frac{sqrt{3}}{2}$

Coordinates:

$oxed{left(-frac{1}{2}, -frac{sqrt{3}}{2}
ight)}$

Start Using PopAi Today