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- Date Submitted: 01/02/2016 08:17 AM
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Mathematical Exploration of Trig
Rationale:
While we are learning the trignometry unit, we are given two kinds of way to measure the angles. One way is degrees and the other way is radian. We are using both degrees and radians to describe angles is not because people are idle to do nothing but because different ways are created in different places in different time for different intends. So, which do you think is more used in trignometry?
Degrees
Degrees is the first unit being taught to measure angles. The concept of angles can data back to the culture of Babylon in Mesopotamia. The Babylonians specialize in astronomy, which is also the origins of how they create the degrees. The Babylonians figure out that when at equinox, the track that the sun goes is around 180 diameters of sun so they rule the circumference as 360 degrees. The sign ° represents sun at that time.
Radian
The reason why radian is created is because people are considering to use different unit to describe radius and angles. Euler uses a unit circle and the arc length of a half circle is π and sinπ=0. The same principle, the arc length of a quater circle is π/2 and sin(π/2) =1. From then, people estalbish to use radian to describe the angles.
Why two?
In daily life, compare 90 degrees with π/2, it is easier for us to realize 90 degrees is perpendicular. The degrees system in creasted through observing a part of life so it is easy to recongize. The degrees system has a actual unit so it can calculate with real number while radian can’t.
For radian, it is created to have a more formal unit to represent while studying Maths so it is created for acedemic areas. For instance, when we study calculus in the future, without radian it will be a huge task for us.
Conclusion
People have different ways to describe angles in order to provide convenience for people not only for daily life but also acedemic areas. We should use it properly in our life.
Rationale:
While we are learning the trignometry unit, we are given two kinds of way to measure the angles. One way is degrees and the other way is radian. We are using both degrees and radians to describe angles is not because people are idle to do nothing but because different ways are created in different places in different time for different intends. So, which do you think is more used in trignometry?
Degrees
Degrees is the first unit being taught to measure angles. The concept of angles can data back to the culture of Babylon in Mesopotamia. The Babylonians specialize in astronomy, which is also the origins of how they create the degrees. The Babylonians figure out that when at equinox, the track that the sun goes is around 180 diameters of sun so they rule the circumference as 360 degrees. The sign ° represents sun at that time.
Radian
The reason why radian is created is because people are considering to use different unit to describe radius and angles. Euler uses a unit circle and the arc length of a half circle is π and sinπ=0. The same principle, the arc length of a quater circle is π/2 and sin(π/2) =1. From then, people estalbish to use radian to describe the angles.
Why two?
In daily life, compare 90 degrees with π/2, it is easier for us to realize 90 degrees is perpendicular. The degrees system in creasted through observing a part of life so it is easy to recongize. The degrees system has a actual unit so it can calculate with real number while radian can’t.
For radian, it is created to have a more formal unit to represent while studying Maths so it is created for acedemic areas. For instance, when we study calculus in the future, without radian it will be a huge task for us.
Conclusion
People have different ways to describe angles in order to provide convenience for people not only for daily life but also acedemic areas. We should use it properly in our life.