All Trigonometric Formulas

The trigonometric formulas are and identities are equalities that involves trigonometric functions. The trigonometric formulas are the functions of angles. The basic trigonometric functions are Sine , Cosine and Tan. The sine value takes an angle and it gives the   length of the y component. The cosine function takes an angle and gives the length of the X-component. The tan Value gives the slope of the angle. Normally the trigonometric functions defined by the two sides of the right angle triangle.

 

All Trigonometric Formulas

 

        We can write the trigonometric functions using a right angle triangle

                        Sin value of the angle = Opposite / Hypotenuse

                        Cos value of the angle = Adjacent / Hypotenuse

                        Tan of the angle = Opposite / Adjacent

         Based on these we are defining the trigonometric formulas

         There are Five types of trigonometric formulas                  

                          I) Sum and difference formula

                          II) Double Angle Formula

                          III) Triple angle formula

                          IV) Half angle formulas

                          V) Sum of product formula

 

Sum and Difference formulas:

                          Cos( A+B ) = CosA CosB - SinA SinB

                          Cos ( A-B ) = CosACosB + SinA SinB

                           Sin ( A+B ) = SinA CosB + CosA SinB

                           Sin ( A-B ) = SinA CosB- CosA SinB

                           Tan ( A+B ) = (TanA + TanB) / (1 - TanA tanB)

                            Tan ( A-B ) =  (TanA- TanB) / (1+TanA TanB)

 

all trigonometric formulas-Double Angle Formula:

 

                         Sin2A = 2 Sin A Cos A

                         Cos 2A = Cos2A - Sin2A

                         Cos 2A = 1 - 2Sin2 A

                         Cos 2A = 2Cos2A - 1

                        Tan 2A = 2 Tan A / (1 - Tan2 A)

Triple Angle Formulas:

                        Tan 3A = (3 Tan A - Tan3A) / (1 - 3 Tan2 A)

                         Sin 3A = 3 Sin A - 4Sin3A

                         Cos 3A = 4Cos3A - 3 Cos A

Half Angle Formulas

                       Sin2 (A / 2) = (1 - Cos A) / 2

                       Cos2 (A / 2) = (1 + Cos A) / 2

                        Tan2 (A / 2) = ((1 - Cos A) / 2) / ((1 + Cos A) / 2)

Product of Sum Formulas:

                         Sin A Sin B = [Cos (A - B) - Cos (A+B)] / 2

                         Cos A S Cos B = [Cos (A + B) + Cos (A - B)] / 2

                         Sin A Cos B = [Sin (A + B) + Sin (A - B)] / 2

                         Cos A Sin B = [Sin (A + B) - Sin (A - B)] / 2