Unit Circle
Unit Circle
Unit Circle
It is a circle with a radius of 1 unit. This is very useful for calculating trigonometric ratios.
Here,
O is the center.
A is any point on the circumference of the circle.
B is the perpendicular from A to the x-axis.
E is the x-intercept of the unit circle.
C is the x-intercept of the tangent drawn to the circle at A.
D is the y-intercept of the tangent drawn to the circle at A.
Sine
Therefore sin theta is equal to the length of AB or the value of the y coordinate of the point A.
Cosine
Therefore cos theta is equal to the length of OB or the value of the x coordinate of the point A.
Coordinates of A
Coordinates of A is () given it is any point on the unit circle where theta is the angle formed between A, O, and the X-axis.
Cos theta = x
Sin theta = y
Sec theta = 1/x
Cosec theta = 1/y
Tan theta = x/y
Cot theta = y/x
where x and y are the coordinates of sin theta.