In , a unit circle is a of unit —that is, a radius of 1. Frequently, especially in , the unit circle is the circle of radius 1 centered at the origin (0, 0) in the in the .
The cosine and sine of angle θ may be defined on the unit circle as follows:
If (𝑥, 𝑦) is a point on the unit circle, and if the ray from the origin (0, 0) to (𝑥, 𝑦) makes an θ from the positive x-axis, (where counterclockwise turning is positive), then
cos θ = 𝑥 and sin θ = 𝑦
Note: Because we’ve entered the trigonometry side of maths, the circle starts at Proud on the wheel and we are turning counterclockwise. So it goes from Proud to Confident, to Satisfied, etc... 😊