Trigonometric Circular Function

Trigonometric functions are also known as circular functions due to their origination from circular dimensions in the form of a triangle. Circular functions are based on a right-angled triangle with three sides: base, height, and hypotenuse. The circular function is a relation that binds an angle of this right angle triangle with the other two sides in a ratio. This article discusses the concept of circular functions, also known as trigonometric functions, along with a comprehensive piece of knowledge on different circular functions in mathematics. Furthermore, this article will deliver comprehensive knowledge on six circular functions calculators to ease your problem-solving.

Circular functions

Circular functions are also known as trigonometric functions in mathematics. The term circular reflects the relationship of these functions with a circle. The key concept of trigonometric functions is derived from a circle by taking a pie of circles in the form of a right-angled triangle. The three sides of a right-angle triangle are base, height, and hypotenuse. The relation of two of these three sides with a ratio gives the formula for the circular functions. Now that you have understood the concept of circular functions, you have become familiar with the origination of trigonometric functions. Let us move on to understand different types of circular functions with a detailed guide for a better understanding. 

Different circular functions

In mathematics, there are 6 different circular functions with different identities and formulas and are of great importance in basic and advanced mathematics. These six circular functions are

• Sine

• Cosine

• Cosec

• Tangent 

• Secant

• Cot.

Now that you have become familiar with different circular functions. Let’s move forward and understand each of the circular functions in detail. 

1. Sine

Sine is the ratio of height and hypotenuse of a right-angle triangle. 

2. Cosine

Cosine is the ratio of base and hypotenuse of a right-angle triangle

3. Cosec

Cosec is the ratio of hypotenuse and height of a triangle. It is also the reciprocal of sine. 

4. Tangent

Tangent is the ratio of height and base of a right-angle triangle.

5. Secant

Secant refers to the ratio of hypotenuse and base of a right-angled triangle.

6. Cot

Cot is the abbreviation of cotangent, and it refers to the ratio of base and height of a right-angle triangle. It is the reciprocal of the tangent.

Now that you have understood and become familiar with the six circular functions. Below is a table to provide a comprehensive understanding of different circular functions in mathematics. 

Inverse circular functions

Inverse circular functions are also known as inverse trigonometric functions. In mathematics, these functions are also known as arcus functions. These are referred to as the inverse of the six circular functions discussed above in the table. Now that you have understood the concept of trigonometric functions in detail. Let us move on to this article’s next topic, namely inverse circular functions. The inverse of any circular function is used to get the angle from its trigonometric ratio, and these arcus functions are used in geometry, engineering, navigation and physics. Below is the table to familiarise you with the name, notation, definition, domain, and range in radians and degrees.  

Conclusion

There are six circular function calculators to evaluate the formula and process of computing the value of circular functions in a right-angled triangle. The concept of circular functions helps solve complex problems of mathematics and real-life applications. Circular functions are derived as a ratio of two sides of a right-angle triangle for a particular angle, and the placement of these angles and sides depends on each other. Sine, cosine, tan, cosec, sec and cot are six different circular functions. This article has covered a comprehensive guide to circular functions, formulas, and other important information.