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# Unit Circle

Trigonometry unit Circle is a circle which has radius one. The equation of Unit Circle is x2 + y2 = 1. The graph of the unit circle is shown below:

Following steps will help us to draw the circle:

As it is already described in the definition that unit circle has the radius one, so check whether the radius of the circle is one or not. The next step is to plot the Tangent and then find the equation of the unit circle by using pythagoras theorem. Now for the Right Angle triangle Square of the longest side must be equal to the square of the rest of two sides. Hence this will give us the equation of unit circle.

As we know circle is an enclosed loop in which every Point on the path is equidistant from the center. Circles are the part of analytical Math. The analytical Trigonometry is the extended part of right angle triangle trigonometry. Now again coming to the circle there are some basic properties such as:
Radius: It is a line segment from a center to the point on the path of circle.

Chord: It is a Straight Line made with the two points on the path of the circle.

Diameter: It is the twice of the Line Segment from a center to the circular path or radius.

In trigonometry there are six trigonometric Functions: sine, cosine, tangent, cotangent, secant, cosecant, where cosecant is the reciprocal of sine, and cotangent of tangent and secant of cosine respectively.
Suppose a point (x, y) on unit circle and has Ray from the origin (0, 0) to (x, y) forms the angle ‘z’ from the positive axis then:
cos z = x,
sin z = y,
Then the equation x2 + y2 = 1 gives the relation
cos2 (z) + sin2 (z) = 1.

UNIT CIRCLE CHART

Unit circle can be defined as a circle that has radius equals to one. Equation of unit circle is given as:
P2 + Q2 = 1. Unit Circle Chart is given as:

 s.no Ó¨ (rad) Ó¨0 Sin Ó¨ Cos Ó¨ tanÓ¨ = sinÓ¨ / cos Ó¨ 1 0 Đ› / 6 0 30 √0 / 2 = 0 √1 / 2 = 1 / 2 √4 / 2 = 1 √3 / 2 √0 / √4 = 0 √1 / √3 = √3 / 3 2 Đ› / 3 60 √3 / 2 √1 / 2 = 1 / 2 √3 / √1 = √3 3 Đ› / 2 90 √4 / 2 = 1 √0 / 2 = 0 ---- 4 2Đ» / 3 120 √3 / 2 -√1 / 2 = -1 / 2 √3 / -√1 = -√3 5 5Đ» / 6 150 √1 / 2 = 1 / 2 -√3 / 2 √1 / -√3 = -√3 / 3 6 Đ› 180 √0 / 2 = 0 -√4 / 2 = -1 √0 / - √4 = 0 7 7Đ» / 6 210 -√1 / 2 = -1 / 2 -√3 / 2 -√1 / -√3 = √3 / 3 8 4Đ» / 3 240 -√3 / 2 -√1 / 2 = -1 / 2 -√3 / -√1 = √3

## Circular Functions

We are here to discuss the circular Functions. A Circle is defined in the form of an equation as x2 + y2 = 1. This is a basic equation of a circle. Here x and y are two axes which are used to define the Position of a circle.

In given example Point p is telling the position of x and y axis. Here sinq= y, cosq = x.
So we can find another circular function also. As