The Unit Circle Learning

A unit circle is a circle with a radius of one. Especially in trigonometry, the unit circle is the circle of radius one centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.The point x, y the unit circle in the first quadrant, they are the lengths of the legs of a right triangle whose hypotenuse has length 1.

x2 + y2 = 1.

(Source: Wikipedia)



Definition for unit circle learning:


A reference value of a quantity used to express other values of the same quantity. Circle with radius unity. Its area is П and circumference 2 П.

It is a plane curve formed by the set of all points of a given fixed distance from a fixed point. The fixed point is called the centre and the fixed distance the radius of the circle. A circle is a locus of a point whose distance from a fixed point is constant.

The diameter of a circle is double of its radius. The circumference is 2 П r and its area is Пr2. The equation of a circle with radius r and centre at origin in Cartesian coordinate is x2 + y2.= r2




Explanation and application for unit circle learning:


Explanation for unit circle learning:

1 Length of circumference:

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

C = 2 `pi`r

Diameter d = 2r

`pi` = Circumference of a circle / diameter of the circle

`pi` = 3.14

C =  `pi` d

2. Area enclosed the circle:

Area of the circle =  `pi` r2

Area of the circle interms of diameter

A =  `pi` (d / 2)2          (d – diameter, r – radius)

Area =  `pi` d2 / 4         ( `pi`– 3.14)


Application of the Unit Circle learning:

The most important function of unit circle is the implementation of trigonometric ratios over the unit circle.
And it shows the relative of unit circle and the trigonometric ratios.
It is used to understand the relationship between the unit circle and the trigonometric (sine and cosine) functions.
Because of this explanation it is use to solve a real-world application.