Unit Circle

In mathematics, a unit circle is a circle with a radius of one. The unit circle can be used in trigonometry, when placed in a Cartesian coordinate system, so that its center is at the origin (0,0).

Now, if we have (x,y) as a point on the unit circle, and knowing that the radius of the circle is equal to one, we may form a triangle and therefore acquire a equation, called the equation of unit circle: x² + y² = 1.  

Now, let's get more into trigonometric function of the unit circle. If we have a point on the unit circle (x, y) and we form a triangle with it, a angle "t" will be formed.

Do you remember the definitions of cosine and sine? Well, if you do, you will know that, considering the radius (hypotenuse) being equal one, cos(t) = x and sin(t) = y. We also already know the equation of the unit circle (x² + y² = 1). Now let's sub the x and y with cos and sin. This will result in cos²(t) + sin²(t) = 1   

Knowing this equation, it is easy to determine points and angles on the unit circle. However, to be more practical you must memorise the unit circle, not only the angles, but the radians.