what is sin(a + b) = ?

Question

what is sin (a + b) =
what is the formula to expand??

Answer 1

sin(a + b)
(sin a)(cos b) + (cos a)(sin b)

example:

sin(45 + 30)
coordinates of 45 degrees = [(sqrt of 2)/2 , (sqrt of 2)/2]
coordinates of 30 degrees = [1/2 , (sqrt of 3/2

a = 45 degrees
b = 30 degrees

plug in the coordinates. remember that sin = y value and cos = x value

[sqrt of 2)/2][1/2] + (sqrt of 3/2][(sqrt of 2)/2]
[sqrt of 2]/4 + [sqrt of 6]/4

answer = (sqrt of 2)+(sqrt of 6) / 4

Answer 2

= sin a.cos b + cos a.sin b
Example
sin (60 + 30)° = sin 90° = 1
= sin 60°. cos 30° + cos 60°. sin 30°
= (√3 / 2).(√3 /2) + (1/2).(1/2)
= 3 / 4 + 1 / 4
= 1 as required

Answer 3

= sin(a)*cos(b) + sin(b)cos(a)

or look in any trig text