Is there a relation between angle and time?

Angle is angle. Time is time. What is their relationship, if any?

The answer is important in the study of trigonometry.

Trigonometric expression can be written 2 ways:

sin A
sin 2 p f t

So there must be some relation between angle and time since the trigonometric function can be written both ways having angle and time within them.

Let me explain.

1 round or cycle can be taken as 360⁰ or 2 p.

For 2p f t,

"f" or frequency means number of cycles per second.
When f = 1 ==> 1 cycle per second.

"t" means time taken to cover the cycle in second.

If f = 1 and t = 0.5 second, then number of cycles taken = f x t = 1x 0.5 cycle or half a cycle.

If f = 2 and t = 0.5 second, then number of cycles taken = 1 cycle of 2p.

Therefore, the time taken (t) decides also the number of cycles covered. The number of cycles covered also means the angle (A) covered. The more time taken, the bigger is the angle covered.

From the deduction above, we can conclude that angle (A) is proportional to time (t) used up.

Therefore we can express the trigonometric functions with both angle and time as the computation factor.

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