Trigonometry is one of the most significant branches of mathematics. Trigonometry is one of those topics which requires a lot of determination and hard work. Trigonometry demands regular practice from students. It is taught to students of higher classes. It is one of those topics that requires basic knowledge of mathematics along with presence of mind. This branch of the topic deals with angles of the right angled triangle. In trigonometry, students study different angles like sin, cosine and unit circle.
This article deals with the unit circle and trigonometry and the application of unit circles in everyday mathematics.
First of all, let’s discuss what a unit circle is.
It can be defined or termed as the circle which has a radius equal to one. The unit circle is always plotted in the cartesian coordinate plane. It is a type circle that is algebraically recognized using the second-degree equation with two variables, x and y. Trigonometry is incomplete without the unit circle, as it is useful in getting the values of the trigonometric ratios like sin, cos and tan.
In simple words, it can be termed as the locus of a point that lies in a fixed distance of one unit from a fixed point. This type of circle is termed a unit circle.
The equation of the following circle is equal to
x2 + y2 = 1 where the centre of the circle is equal to (0,0) and radius equal to one.
These were some of the basic definitions regarding unit circles.
Listed below are some of the applications of the unit circle in one’s life.
- The basic properties and concepts of the unit circle are used in physics and mathematics for decoding vectors into their components. Unit circle has to play a vital role in this. Without the help of a unit circle, it would be very difficult for students to find out the components.
- The unit circle is a circle of radius one unit measure, whose centre lies at the origin of the coordinate system. This circle helps in finding out the output of the trigonometric functions for all real numbers.
- The unit circle is used in the Euler formula.
Euler’s Formula gives the point on the unit circle in the complex plane when an angle is already given.
- Unit circle is really necessary for changing a point from the Polar Coordinate System to the Cartesian Coordinate System. The functions sine and cosine are used to take out the x and y components of the adjacent point. This can be only possible with the help of a unit circle.
- The sine function gives the sine of a number provided in radians. In geometrical terms, the function gives back the vertical component of the point, which is formed by the angle on the unit circle. The function returns in the ratio of the opposite side to the hypotenuse side.
- The cosine function results in the cosine of an angle which is provided in radians. Geometrically, the trigonometric ratio is determined by the ratio of the right-angled triangle’s adjacent side over its hypotenuse of the triangle.
- When the given angle of a right triangle as input returns the ratio of the triangle’s opposite side over its adjacent side, then it is termed as the tan theta of the triangle. This can be possible with the help unit circle; a unit circle is a key factor that will help in finding out all the trigonometric ratios.
These are the applications of the unit circle in one’s life. With the help of trigonometry, the life of the people has become completely changed. The unit circle and trigonometry go hand in hand.
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