UnbelievableDreams one year ago Confusing math question

1. mathstudent55

sin(x/2) = (sqrt (3))/2 Where is the sin theta equal to sqrt(3)/2 ?

2. mathstudent55

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3. mathstudent55

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4. mathstudent55

Keep in mind, all this is x/2, not x yet.

5. UnbelievableDreams

So it is {pi/3 + 4npi , 2pi/3 + 4npi} ?

6. mathstudent55

If $$\sin \theta = \dfrac{\sqrt 3}{2}$$, then $$\theta = \dfrac{\pi}{3} + 2\pi n$$ or $$\theta = \dfrac{2\pi}{3} + 2\pi n$$ The equation had $$\sin \dfrac{x}{2}$$, so now we let $$\theta = \dfrac{x}{2}$$ and solve for x. If $$\theta = \dfrac{x}{2} = \dfrac{\pi}{3} + 2\pi n$$ $$x = \dfrac{2\pi}{3} + 4\pi n$$ or $$\dfrac{x}{2} = \dfrac{2\pi}{3} + 2\pi n$$ $$x = \dfrac{4\pi}{3} + 4\pi n$$