Sine Addition Formula

The Sine Addition formula states that:

  sin(a+b)= sina cosb + sinb cosa

Or

sin(a-b)= sina cosb - sinb cosa

We can see if this works by plugging in some angles.

Lets say that a= 30 and b=60.

            Sine Addition Formula:     sin(a+b)= sina cosb + sinb cosa   

            Equation:             sin(30+60) = sin(30)cos(60)+sin(60)cos(30)

            simplify 30+60            sin(90) = sin(30)cos(60)+sin(60)cos(30)

            calculate sin90                   1 = sin(30)cos(60)+sin(60)cos(30)

            calculate sin30                   1 = 0.5 *cos(60) + sin(60)cos(30)

            calculate cos60                  1= 0.5 * 0.5 + sin(60)cos(30)

           calculate sin60                    1= 0.5*0.5 + v3/2 * cos30)

            calculate cos30                  1 = 0.5 *0.5 + v3/2 * v3/2

            calculate 0.5 * 0.5              1= 0.25 + v3/2 *v3/2

           calculate (v3/2)²                 1= 0.25 + 0.75

           solve                                         1=1

Since 1 does equal 1, the sine addition formula is accurate.