It is a circle with a radius of 1 unit. This is very useful for calculating trigonometric ratios.[br]Here, [br]O is the center.[br]A is any point on the circumference of the circle.[br]B is the perpendicular from A to the x-axis.[br]E is the x-intercept of the unit circle.[br]C is the x-intercept of the tangent drawn to the circle at A.[br]D is the y-intercept of the tangent drawn to the circle at A.

[math]sin\Theta=\frac{opp}{hyp}=\frac{AB}{OA}=\frac{AB}{1}=AB[/math][br]Therefore sin theta is equal to the length of AB or the value of the y coordinate of the point A.

[math]cos\Theta=\frac{adj}{hyp}=\frac{OB}{OA}=\frac{OB}{1}=OB[/math][br]Therefore cos theta is equal to the length of OB or the value of the x coordinate of the point A.

Coordinates of A is ([math]cos\Theta,sin\Theta[/math]) given it is any point on the unit circle where theta is the angle formed between A, O, and the X-axis.[br][br]Cos theta = x[br]Sin theta = y[br]Sec theta = 1/x[br]Cosec theta = 1/y[br]Tan theta = x/y[br]Cot theta = y/x[br]where x and y are the coordinates of sin theta.[br]