Andy C. answered • 08/03/17

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What is the domain of x?

As you know, IVT guarantees sine function is zero at 0 and pi.

That will give you the root you want.

Will suffice to show that x = -theta along that interval.

sin(x+theta) = sinx*cos(theta) - cosx*sin(theta)

At theta=0 : the expression is sin x

At theta=pi/2: the expression is -cos

At theta=pi: the expression is -sin

Sine function is positive in quadrants 1-2, so there is a

nice, clean, and crystal clear sign change

in the angle addition expression for sin(x+thetha) in that interval

IVT guarantees a root.

end of proof

Shahram S.

_{i}and a_{i}are given for every i. Therefore, we don't have just one theta but there are K of them within the summation. Domain of x is real numbers by the way.08/03/17