How to Explain the Unit Circle? – Definition

What do you understand and know about unit circle? A unit circle is a circle centered at the origin with a radius of one.

Unit Circle’s Formula:- x2 + y2 = 1

This equation is important because this will be used as a tool to model periodic phenomena.

Applications of Unit Circle in Real Life

Circles are used for various applications such as architecture, gardening, graphics, infrastructure, transportation.

  • We use circles to make spheres such as ball bearings, cylinders such as cans to preserve food, and cups for drinking and cones.
  • It is even used in gardening to figure out how much space does a plant requires to grow.
  • Circles are also used in engineering such as in gears for automobiles.
  • It is also used in graphics for the rotation of objects on a computer screen.
  • Even used for calculating the distance that a car has traveled.

How to Memorize a Unit Circle?

The best way to memorize a unit circle is to remember that sin is X, cosine is Y, and tan is Z. Add those to the factor that the unit circle always has a radius of 1 and you can determine the unit circle.

Why are Unit Circles Important?

Just like with a unit vector, the unit circles are important for simplifying problems with large numbers. If you can simplify the problem down to a unit circle with a radius of 1, then you can compare the values of circles with different sizes.

How to Calculate a Unit Circle?

Here are the steps to be followed:-

  • Measure the angle of the unit circle. 
  • Calculate the value of sine (X)           
  • Calculate the value of cosine (X)
  • Calculate the value of tangent of (X)

Interesting Facts about a Unit Circle

  • We use the unit circle for many things in life, we never think about it and how it gets applied to such things. Here are some examples of how and when we use it. When we explain the width of a river, about a cop and a car crash, and sonar equipment from the military. All these things happen in everyday life and they use mathematical theory to relate to the unit circle.
  • One real-life situation is that the pi radians are useful to the cop in figuring out where the attacker came from or what happened in a car crash.
  • Another real-life situation that pi radians are useful for is in the military dealing with their sonar or radar equipment. It could tell them how and where on the circle plane an aircraft is located.
  • Do many people buy pizzas without knowing how the pizza was cut? The person who has the job of cutting the pizza has to use a unit circle to cut it right.

Trigonometry- Definition

By the word “trigonometry“, what do you think it is all about? It is a branch of mathematics concerned with specific functions of angles and their application to calculations.

There are 6 functions of an angle commonly used in trigonometry. Their names and abbreviations are:-

  • Sine (Sin)
  • Cosine (Cos)
  • Tangent (Tan)
  • Cotangent (Cot)
  • Secant (Sec)
  • Cosecant (Csc)

Classification of Trigonometry

Trigonometry is classified into two sub-branches and they are:-

  • Plane Trigonometry
  • Spherical Trigonometry 

Trigonometry Identities

There are 3 important trigonometric identities and they are:-

  • sin²θ + cos²θ = 1
  • tan²θ + 1 = sec²θ
  • cot²θ + 1 = cosec²θ

Real-Life Applications of Trigonometry

  • It can be used to measure the height of a building and mountains
  • Used in video games as well
  • Used in construction
  • It is even used in in-flight engineering
  • It is used in even studying physics
  • Archeologists use trigonometry
  • Even used in criminology
  • Trigonometry is even used in marine engineering
  • Used in navigation

There are many other interesting facts about mathematics that we don’t know that relate to our day-to-day life.

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