$ ext{Find the Quadrant of a Point on the Unit Circle}$

To determine the quadrant of a point $(x, y)$ on the unit circle, we need to consider the signs of $x$ and $y$. The unit circle is centered at the origin (0,0) and has a radius of 1.

For example, let’s find which quadrant the point $(\frac{\sqrt{3}}{2}, -\frac{1}{2})$ lies in:

1. Since $\frac{\sqrt{3}}{2} > 0$, the x-coordinate is positive.

2. Since $-\frac{1}{2} < 0$, the y-coordinate is negative.

From these observations, we know that the point lies in the fourth quadrant.

So, the point $(\frac{\sqrt{3}}{2}, -\frac{1}{2})$ is in the fourth quadrant.

To determine the quadrant of a point $(x, y)$ on the unit circle, we will analyze the signs of $x$ and $y$. The unit circle is centered at the origin (0,0) and has a radius of 1.

Consider the point $(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$:

1. Since $-frac{sqrt{2}}{2} < 0$, the x-coordinate is negative.

2. Since $frac{sqrt{2}}{2} > 0$, the y-coordinate is positive.

This means the point lies in the second quadrant.

Therefore, the point $(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2})$ is in the second quadrant.

To identify the quadrant of a point $(x, y)$ on the unit circle, we should look at the signs of $x$ and $y$. The unit circle is centered at the origin (0,0) and has a radius of 1.

For instance, consider the point $(-frac{1}{2}, -frac{sqrt{3}}{2})$:

1. Since $-frac{1}{2} < 0$, the x-coordinate is negative.

2. Since $-frac{sqrt{3}}{2} < 0$, the y-coordinate is also negative.

This tells us the point lies in the third quadrant.

Therefore, the point $(-frac{1}{2}, -frac{sqrt{3}}{2})$ is in the third quadrant.

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