What is the exact value of the sum sin x+0.5=?

giorgiana1976 | Student

To find the value of the sum, we'll create matching functions in the given sum.

For this purpose, we'll substitute the value 0.5 by the equivalent function of the angle pi/6, namely sin pi/6 = 0.5.

We'll transform the sum  into a product.

sin x + 0.5 = sin x + sin pi/6 

sin x + sin pi/6  =  2sin [(x+pi/6)/2]*cos[ (x-pi/6)/2]

sin x + sin pi/6  = 2 sin [(x/2 + pi/12)]*cos[ (x/2 - pi/12)]

sin [(x/2 + pi/12)] = sin (x/2)/2 + [2*sqrt3*cos (x/2)]/4

sin [(x/2 + pi/12)] = sin (x/2)/2 + [sqrt3*cos (x/2)]/2

cos[ (x/2 - pi/12)] = cos(x/2)*cos(pi/12) + sin(x/2)*sin (pi/12)

cos[ (x/2 - pi/12)] =  cos(x/2)/2 + [sqrt3*sin (x/2)]/2

sin x + 0.5 = {[sin (x/2) + sqrt3*cos (x/2)]*[cos(x/2) + [sqrt3*sin (x/2)]}/2

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