Study about Unit Circle

In Euclidean geometry the simple shape is called circle and it consisting points in a plane which is middle from a given point called the center. Radius is the distance of the points from the center.

Unit circle:

In geometry, a unit circle is a circle with a radius of one. The unit circle is the radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane except the trigonometry. The higher dimensions is the unit sphere is denoted by s1.

If (x,y ) is the first quadrant of the unit circle, then p and q are the lengths of a right triangle whose hypotenuse has length 1. That is, from the Pythagorean Theorem satisfy the following equation with x and y,

x2 + y2 = 1.

Explanation:


1. Length of circumference:

The circumference’s length is related to the radius (r) by

c = 2`pi` r

diameter d  = 2r

r = 2 / d

c = `pi`d

2. Area enclosed the circle:

Area of the circle =  `pi ` × area of the shaded square

The area of the circle is π multiplied with the radius squared:

A =` pi` r2

Area of the circle interms of diameter

A  = ` pi`(d/2)2

Area =` pi` d2 / 4


Trigonometric functions on the unit circle:




In geometrical term the trigonometric functions of the angle θ can be modified to a unit circle centered at O.

If  a point of the unit circle is (x, y) , and if the origin (0, 0) to (x, y) makes an angle t from the x-axis, in the trigonometric functions like sine, cosine terms.

cos(t) =x

sin(t) = y

The equation x2 + y2 = 1 gives the relation

cos2(t) + sin2(t) = 1

Solution:

Finally from properties of circle we conclude that the circle does not have any number of sides. That is circle have 0 sides.