1. We have learned that in a right angled triangle, how to calculate sin(x) by trignometric ratio.
There are many derivation for that.


But that is for right angled triangle. Now x should be < 90 always.


2. Now how can we apply this to sin(270) or any anle above than or 90.

3. Now proof we have is for right angled triangle. How it could be apply to any angle.

4. How come angle greater than 360 degree possible. e.g we calculate value of sin (510).?

 

hi aamirali,
Look at this link,
http://www.themathpage.com/atrig/functions-angle.htm
E

 

4. How come angle greater than 360 degree possible. e.g we calculate value of sin (510).?

If you are measuring angular velocity then angles greater than 360 are important

eg 1000 rpm = 360, 000 degrees per minute = 6,000 degrees per second.

 

We use the property of the sine function that it is periodic with a period of 360 degrees or 2pi radians. This allows us to compute the sine of any angle from minus infinity to plus infinity. You can also convince yourself this is the case by examining the Taylor series expansion of the sine function.