Trigonometric Formula

Some useful Trignomtric Formulas : Sin A = opposite / hypotenuse Cos A = Adjacent / hypotenuse Tan A = opposite / Adjacent	Law of Sines : Sin A/a = Sin B/b = Sin B/c Law of Cosines : C2=a2 + b2 - 2ab cos C

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Speciality of 0...

Speciality of '0'

0 is a very unique number and it's speciality can started in following points :

       1)    '0' is a whole number as well as Integer.

       2)    '0' can never possess + or - sign because it is been invented for our convenience.

        

               for e.g., :-  0 - 7 = -7, 0 + 7 = 7, -7 + 7 = 0

                  

                               0 x 7 = 0 , 7 x 0 = 0, -7 - 0 = -7

                            

                              7 - 0 = 7, 7 + 0 = 7, 7 - 7  =  0 

          

                              0/7  =  0 but  7/0  ≠ 0 because


it will give answer as '∞' i.e., infinity and which is not an appropriate answer. Hence it is clear from the above 


examples that '0' has been invented just for our convenience while solving mathematical operation and nothing


else.


         3) Every number loses it's value or it becomes zero whenever it is multiplied with '0' or it is dividing


zero..


          4) It is the only number which is the largest number from negative infinity and the smallest from the


positive infinity. It always remains in the center of real number line....    

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How to find whether a large number is divisible by 13 ?

How to find whether a large number is divisible by 13 ?

Lets take an example : Is 377 divisible by 13 ?



Here is trick


37  -  9(7)  =  37  -  63  =  -26


As -26 is divisible by 13  we can say that 377 is also divisible by 13...



Lets take another example  :  Is 2054 divisible by 13 ?



Therefore


205  -  9(4)  =   205   -  36  =  169


Again



16  - 9(9)  =  16  -  81  =  -65



As -65 is divisible by 13 ... The number 2059 is divisible by 13...



Note :  Multiply the unit's place with 9 as in both the above examples....

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