Find all solutions to the equation. sin x = sqrt3/2

Question

vuriffy · Answer

Oh god.

vuriffy · Answer

I could help, but let me open my good ole notebook.

vuriffy · Answer

Oh, I already have this problem done.

vuriffy · Answer

Do you have a calculator by chance?

brydenwright · Answer

Yes

vuriffy · Answer

Okay, 
for sin x = sqrt(3)/2
sin^-1 each side
sin^-1(sin x) = sin^-1 (sqrt(3)/2)
Tell me what you get.

brydenwright · Answer

1.047

vuriffy · Answer

You have your calculator in the wrong format, actually.

brydenwright · Answer

so 60?

vuriffy · Answer

Yes; what is the value of radians at 60?

brydenwright · Answer

pi/4

vuriffy · Answer

pi/4 is for 45.
pi/3 is for 60.

brydenwright · Answer

Oh, that's right. Sorry about that.

vuriffy · Answer

You're fine. So, one of your solutions is pi/3.

vuriffy · Answer

Also, what I learned by myself is: the value of x times the lower number of the = to value is always the amount of solutions. 
so (1) - x * (2) - sqrt(3)/2 
2 solutions.

vuriffy · Answer

Sin of x, only does one loop on the above axis, so the solutions are both before 1 pi.

brydenwright · Answer

$${ \pi/3+n \pi | n=0, +-1, +-2...}$$ is one of the options, would that be it then?

vuriffy · Answer

Next, you shall use the method of the graph to make it easier for you. All you need to do is PI - pi/3 and you get 2pi/3, which is the second solution.

brydenwright · Answer

Okay. I think I get it now. Thanks!

vuriffy · Answer

That was considering the fact of the sin x graph as a whole and also that the rate of distance was pi/3. You're welcome.