Question

Confusing math question

Answer 1

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

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

Answer 2

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

Answer 3

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

Answer 4

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

\(\dfrac{x}{2} = \dfrac{2\pi}{3} + 2\pi n\)

\(x = \dfrac{4\pi}{3} + 4\pi n \)