Expert: Chen Min - 12/18/2008

Question
what is use of sin,cos,cosec,cot?why wwe are using it?also please write me what are the properties of sin,cos,cosec,cot,sec?
please aneswar to my question

please help me to clear my doubts

Answer
This question is rather general, but I'll try to explain it.

Trigonometry is about the six functions: sin, cos, tan, cot, sec, cot.Each representing a ratio between two designated side of a right-angled triangle with respect to the selected angle. You should be clear that the functions are only dependent on the magnitude of the angle. That is to say, sin 30 degrees has a fixed value of 0.5.

They are useful because they can be utilised in many many ways.

Firstly, they relate the two disparate ideas(length and angle). People use them to build a bridge between angles and sides while eliminating all the complex calculations and conversions. Using them greatly simplified the process of solving geometry problems.
e.g. we can express the relation ship between angles and sides in any angle using the sine rule:
 a / sinA = b / sin B = c / sin C = 2R

Secondly, each function has a unique graph which can help solve geometry problems. The sine graph especially, is used to calculate the wave frequency and amplification, like those of X-rays, due to its distinctive wave-like shape.

Thirdly, trigonometry function can solve functional problems. For example, since sine and cosine have values not bigger than 1 and no less than -1, we can use them to substitute any variables that have the same domain.

Also, it helps solve questions like extrima. Functions in trigonometry can be readily combined and altered to provide us with deep insight to the fluctuation of variables and come up with due solutions.

There is no way I can summarise all the utilities and I don't expect you to know everything above. But trust me, there is a long way to go, buddy.

Since the values are decided by the magnitudes of angles, they are either obtained roughly by measuring or using functions like Taylor's theorem. But whatever value the angles take, sine always has the value within -1 and 1, and so do cosine,due to the intrinsic characteristic of right-angled triangles.Others pls explore yourself~