Sin Angle Formula

Sin is a basic trigonometric function. In this article we are going to deal with sin angle formulas and how to use the sin angle formulas. Sin angle formulas used to calculate the sin values of the angles. Using the sin angle formulas we have to find the side lengths of the triangles normally from a right angle triangle we can say the sin function as
Sin A = `(opposite) / (hypotenuse)` . In this A is the angle of the opposite side.

Once you've gone through these, take a look at our Arc Formula for more refernce.

Sin angle formulas:

           There are five types of sin angle formulas are there.
Sum and angle formula
              Sin(X +Y) = Sin X Sin Y + Cos X Cos Y
              Sin (X – Y) = Sin X Sin Y – Cos X Cos Y
Double angle formula
             Sin 2A = 2 Sin A Cos A
Triple angle formula
             Sin 3A = 3 Sin A – 4Sin³A
Half angle formula
             Sin²(X / 2) = ((1 – Cos A) / 2)
Product and sum formula:
             Sin X Sin Y = Cos(X – y) – Cos (X + y) / 2
             Sin X Cos Y = Sin (X + Y) + Sin (X – Y) / 2

Example problems for sin angle formulas:

 Example 1:
      Find the value of 75^o
Solution:
         Sin 75^o = Sin (30^o+ 45^o)               
             We know the sin angle formula
                                        Sin(X +Y) = Sin X Sin Y + Cos X Cos Y
                                        Sin (30^o+ 45^o) = Sin 30^o Sin 45^o + Cos 30^o Cos 45^o
                                        Sin (30^o+ 45^o) = `(1 / 2)xx (1 / sqrt(2)) + (sqrt(3) / 2) xx (1 / sqrt(2))`
                                        Sin (30^o+ 45^o) = `(1 / (2 sqrt(2))) + (sqrt(3) / (2 sqrt(2)))`
                                        Sin (30^o+ 45^o) = `((1 + sqrt(3)) / (2 sqrt(2)))`

Example 2:
         Find the value of Sin 150^o using double angle formula. Where sin 75^o = 0.9659, Cos 75^o = 0.2588
Solution:
         Given sin 75^o = 0.9659, Cos 75^o = 0.2588
         Sin 150^o = Sin 2 `xx` 75^o
           We have the sine angle formula Sin 2A = 2 Sin A Cos A
                 Sin 150^o = 2 Sin 75⁰ Cos 75^o
                 Sin 150^o = 2 `xx` 0.9659 `xx` 0.2588

                 Sin 150^o = 0.4999