# Interactive unit circle

The unit circle is a circle of radius one suspended on any point on the circle’s circumference. The unit circle is used explicitly in trigonometry and is centered at the origin of a Cartesian plane. S1 denotes it because of its one-dimensional structure.

The point to be noted here is that all the trigonometric functions values depend on the unit circle. The interior of the unit circle is known as a unit disk. The word ‘’distance’’ can also describe the nature and the structure of the unit circles. Learn more about Trig identities to clear all the basic knowledge of Trigonometry.

## Interactive unit circle

The interactive unit circle connects the trigonometric functions tangent, cosine, and sine and the unit circle. The unit circle is a circle of radius one suspended in a particular quadrant of the coordinate system. The radius of a unit circle can be taken at any point at the perimeter of the circle. It forms a right-angled triangle. The angle between this unit circle will be represented by angle θ To change a grade, simply click and drag the two control points. This unit circle has three functions.

• Cosine
• Sine
• Tangent

The interaction between this unit circle and its corresponding functions is known as interactive unit circles. Before heading further, let’s first discuss some simple terminologies.

### Sine, Cosine and Tangent

1. Cosine

In a right-angled triangle, the ratio between base and hypotenuse is known as cosineθ. It is the most crucial trigonometric function of all. Mathematically, cosine is obtained by dividing the base of a right-angled triangle with its hypotenuse.

Cosine =    Base/Hyp

•   Secant

The reciprocal of cosine is also used in some triangles. It is known as secantθ and is used in various numerical calculations. It is calculated by reciprocating cosineθ .

Secant=1/cosine

2. Sine

Second and another fundamental trigonometric function is sineθ. Mathematically sineθ  is calculated by dividing the perpendicular of a right-angled triangle with its hypotenuse. Hence we can calculate the length or the angle of any structure with the above relation’s help.

Sineθ = Perpendicular/Hypotenuse

• Cosecant            As of cosine, the reciprocal of sineθ is known as cosecantθ. It is calculated by reciprocating sine  or simply dividing it by 1.

Cosecantθ=1/sinθ

3. Tangent

Third and another fundamental trigonometric function is known as tangent  . As per sineθ and cosineθ, it is also obtained by a right-angled triangle. By dividing the perpendicular of a triangle with its base, we can easily calculate the value of tangentθ . The mathematical formula of tangentθ is:

Tangθ= Perp/Base

• Cot

The reciprocal of Tangentθ  is known as cotθ . The value of cot can be calculated by reciprocating the value of tangent  . The mathematical form of this equation is as stated below:

Cotθ=1/Tangθ

So, all the equations and the trigonometric functions can be understood by the following graph 