In the world of mathematics, the unit circle is considered to be a type of circle that comes with a unit radius that ultimately means that the radius of the circle will be one. This particular concept is very widely utilised in the world of trigonometry and the unit circle will be the circle of radius one that will be centred at origin into the Cartesian coordinate system in the Euclidean plane. In the cases of topology, it is also very well utilised and is also considered to be a one-dimensional unit and sphere. The interior of the unit Circle will always be the open unit disc and it will be combined with the unit circle itself which will be referred to as a closed unit disc. Notions like distance can be perfectly utilised in terms of defining the concept of unit circles and further it is very much important to depend upon this concept for multiple reasons. In the cases of the complex plane, the unit circle can be considered as the unit complex numbers and the set of complex numbers Z will be in the form of as explained:
Z = e ^ it = cos t + sin t = cis (t)
This particular relation will also help in representing Euler‘s formula and in the world of quantum mechanics, this is also referred to as the phase vector. The trigonometry functions are also based upon the concept of the unit circle and are very much successful in terms of fulfilling different kinds of purposes. This is a very important concept to be known by the kids nowadays so that they can have a good command over this chapter and ultimately end up scoring well in the examination. This is considered to be one of the best possible ways of learning about the length and angles and the centre will be put on a graph where X and Y axis will cross so that people can get a very neat arrangement throughout the process. Because the radius of the circle will be one then trigonometry values like sine, cosine and tangent can be perfectly measured without any kind of problem. The equation for the unit circle formula will be X square plus Y square is equal to 1. To further become experts of this particular area it is also very much important for the kids to register themselves on platforms like Cuemath online because they will be taught by experts of the industry over here who will be very much successful in terms of clarifying different kinds of doubts and will ensure that students will always be able to fetch good marks in the exams.
- What will happen when the angle of theta will be 0°?
In this particular case a comprehensive formula has to be implemented which is explained as follows:
Cos 0° is equal to 1, sine 0° is equal to 0 and tan 0° is equal to 0.
- What will happen if the value of theta is 90°?
In this case, the formula will be implemented that is explained as follows:
Cos 90° is equal to 0, sine 90° is equal to 1 and tan 90° will be undefined.
Apart from this students also need to be very much clear about the concept of the Pythagoras theorem which is associated with this so that they can solve different kinds of questions very easily and without any kind of problem. Also, it is the responsibility of the students to be clear about the concept of the whole circle because they will need the values in every quadrant with the help of this concept which has to be represented in correct plus or minus sign as per the Cartesian coordinates. Hence, the unit circle formula is also very much important to be memorised by the people and the formula has been explained as follows:
The general equation will be X minus H whole square plus Y minus K whole square is equal to R square