1) Direct number in degree, example, 450
2) Direct number in radian, example, p / 4
3) Frequency based, example 2pf t
The first version needs no elaboration as it is the most common type of angle presentation.
The second version can be obtained from the degree form through the conversion equation:
3600 = 2p (This is basic and and a must to know).
Therefore 450 = (2p / 360) x (45)0 = p / 4
Likewise the vice versa can also be done.
p / 2 = (360 / 2p) x p / 2 = 900
The unit for the second angle version is "radian".
The third version is more for electronic communication application.
The format 2pft has the component of frequency(f) within.
Frequency (f) also means "number of cycles per second"in unit "Hertz, Hz" .
The "t" in this form represents the time (sec) taken in the rotation within a circle.
Note: f = 1 / t
If the time taken is a quarter that to complete one cycle (2p), then angle = 2p (1/t)(t/4) = p / 2 .
Depending on angle usage or applications, their form has to change to suit the solving method.
- If the application calls for the analysis of height with respect to speed of rotation, then the third version is the appropriate one.
- If the application calls for angle measurement, given length of height and base, then the answer can be in the first version.
Thus, judgement is needed and applied in order to use the appropriate form. Math is thus a process where judgemental skill is trained.
Interesting, right? No wonder math is a must in school curriculum.