The unit circle is a circle with a radius of 1 unit that is centered at the origin (0, 0) of a coordinate plane. The equation of the unit circle is x² + y² = 1. It is a commonly used tool in mathematics, especially in trigonometry, as it helps in visualizing the relationship between angles and the coordinates of the circle.
Here is an image of the unit circle:
In this image, the circle is drawn in black, and the x- and y-axes are drawn in blue and red respectively. The angles are measured in radians and are shown in the smaller circle on the inside of the unit circle. The points on the circle are labeled with their coordinates (x, y), which represent the cosine and sine of the corresponding angle, respectively. For example, the point (0.5, 0.866) represents an angle of 60 degrees (Ï€/3 radians), as cos(Ï€/3) = 0.5 and sin(Ï€/3) = 0.866.