Saturday, April 13, 2013

I want to calculate sin 30-cos 60. Can i calculate sin30-cos60=30-60?

No please. It is not correct to calculate sin30 - cos60 as
30 - 60. The concept is totally different.


If ABC is a
right angled triangle with right angle  at B, then sine and cosine ratios are defined 
as below:


sin A = Opposite angle / hypotenuse =
 BC/AC


cosC = Adjascent angle/hypotenuse
= BC/AC.


Therefore in a right angled triangle if A = x,
then C = (90-x) .


Therefore sin A =
sinx


sinx = BC/AC...(1).


cosC
= cos(90-x).


cos(90-x)  =
BC/AC....(2)


Therefore  from (1) and (2) we
get:


sinx =
cos(90-x)....(3).


If  we put x= 30 in eq (3), we
get:


sin30 = cos(90-30) =
cos60.


Therefore,  sin30 - cos60 =
0..


Therefore sin30 -cos60 = 0 and   it is not 30
-60.

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