Trigonometry and its Relationship With Unit Circle

by Maisie

Trigonometry is one of the most important concepts of mathematics. It is the sub-field of mathematics that deals with the study of sides and angles of a right-angled triangle. The word trigonometry has been derived from the Greek word, the meaning of which is a measure of a triangle. The subject of trigonometry has its origin from the Hellenistic world where it was developed from the applications of geometry and astronomical studies. The mathematicians of India are credited to have created the very first known tables of the values for the trigonometric ratios. The Surya Siddhanta was made by the famous mathematician, Aryabhata where sine convention and its properties were documented. The concept of unit circle has a relationship with trigonometry. In this article, we will discuss its relationship. We will also find out about the applications of trigonometry.

What Do You Mean by Unit Circle?

Unit circle as the name suggests is a circle having a radius of one unit. A two-dimensional geometric figure that does not have any sides and angles is known as a circle. All the properties of a circle are present in a unit circle and its equation is also derived from the equation of a circle. The concept of a unit circle can be applied to find out the values of the trigonometric function ratios. Talking specifically, the values of sine, cosine, and tangent can be derived from the help of a unit circle. In a cartesian coordinate plane, the Pythagoras theorem is applied to derive the values of these functions.

Trigonometric Ratios

The trigonometric ratios can be defined as the values which are related to the functions of trigonometry which is based on the ratio of the sides of a triangle that is right-angled. Basically, there are three sides to a right-angled triangle. The side which is opposite to the base and the perpendicular is known as the hypotenuse which is also regarded as the longest side of a triangle. The side opposite to the angle is known as the perpendicular and the side which is adjacent to the angle is defined as the base. Talking about the ratios of trigonometry, there are a total of six ratios such as sine, tangent, cos, cotangent, cosecant, and secant.

Application of Trigonometry

Trigonometry is a part of mathematics that so occupies the position of the subject mathematics in comparison to others. The trigonometric functions and their properties have numerous applications in our everyday life. The applications of trigonometry range from satellite navigation to the formation of computer music. The following points mentioned below analyze the trigonometric application in a detailed manner. Some of them are as follows:

  1. The trigonometric applications are more often than not used in the measurement of the height and building or mountain etc. We can measure the distance with the help of the viewpoint and the elevation angle of the building.
  2. Nowadays we see a  lot of crime scenes, the trigonometric functions help the crime investigators to determine the projectile, and also determine the cause of the collision effect.
  3. Trigonometry is mostly used in the other parts of mathematics such as calculus and algebra. The trigonometric function is also used to determine the sound and light waves using the sine and cosine functions.
  4. You might have heard about the effect of sunlight in the process of photosynthesis, the marine biologist uses trigonometry in order to calculate the depth of the effect.
  5. The use of trigonometry in aviation technology has been widely used nowadays. We all know that the wind plays a very significant role in the movement of airplanes, the functions of trigonometry can be used here.

If you want to learn about trigonometry and unit circle in a detailed manner, a fun way, and an interactive way, you may visit the Cuemath website.

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