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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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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