Understanding the Unit Circle

The unit circle is a helpful tool for learning about angles. Here’s how it works:

1. What Are Angles?
   Angles can be measured in two ways: degrees and radians.

   • A full circle is 360 degrees.
   • In radians, that same circle is called $2\pi$.

2. Points on the Circle
   Every point on the unit circle has coordinates in the form of $(x,y)$.
   These points are connected to the cosine and sine of an angle, which we call $\theta$:

   • The x-coordinate is $x = \cos(\theta)$.
   • The y-coordinate is $y = \sin(\theta)$.

3. Important Angles to Know
   Here are some key angles and their coordinates:

   • At $0^\circ$ (or 0 radians), the point is $(1, 0)$.
   • At $90^\circ$ (or $\frac{\pi}{2}$ radians), the point is $(0, 1)$.
   • At $180^\circ$ (or $\pi$ radians), the point is $(-1, 0)$.
   • At $270^\circ$ (or $\frac{3\pi}{2}$ radians), the point is $(0, -1)$.
   • At $360^\circ$ (or $2\pi$ radians), we return to $(1, 0)$.

By knowing these positions on the unit circle, it becomes easier to understand and solve trigonometric problems, which are useful in real life!