To understand sine, cosine, and tangent on the unit circle, let’s first talk about what the unit circle is.

The unit circle is a circle that has a radius of 1 and is located right in the center of a graph at the point (0, 0).

Now, here’s how we can look at sine, cosine, and tangent:

1. Sine ($\sin \theta$): This shows the height of a point on the circle.

   • For example, when the angle is $30^\circ$ (or $\frac{\pi}{6}$ in another way of measuring), the sine value is $\sin 30^\circ = \frac{1}{2}$. This means that the height is half of the circle’s radius.

2. Cosine ($\cos \theta$): This shows how far a point is from the center, but side to side.

   • At $30^\circ$, the cosine value is $\cos 30^\circ = \frac{\sqrt{3}}{2}$. This means that the point is about 0.866 units away from the center.

3. Tangent ($\tan \theta$): This takes sine and divides it by cosine.

   • So, $\tan \theta = \frac{\sin \theta}{\cos \theta}$. For $30^\circ$, this gives us $\tan 30^\circ = \frac{1}{\sqrt{3}}$.

Using these values, we can draw these functions on a graph. This helps us see how they all connect to each other!