Determine the general solution to `sin(x/2)= sqrt(3)/2` . Use radians as the unit.

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thilina-g eNotes educator| Certified Educator

`sin(x/2) = sqrt(3)/2`

The primary solution for `(x/2)` is `pi/3` .

Let's now find the general solution for `(x/2)` .

The general solution for sine is given by the following equation.

`(x/2) = npi+(-1)^n(pi/3)` where `n in Z` .

 

Therefore general solution for x is,

`x = 2npi+(-1)^n((2pi)/3)`

Where `n in Z` .

 

(NOTE: you can solve (x/2) = pi/3 for x and then find genral solution for x. It will give wrong answers.)

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