Hi i just hope you can help me, i really try my best but sometimes i just cant!?

Question

Determine the general solution to:
Sin x/2 = (square root of 3)/2
Sorry about the square root thing but i cant find it on my keyboard!

Answer 1

Sin a = (√3)/2 for the angles of a = pi/3 and 2pi/3

So, set x/2 equal to pi/3 and then to 2pi/3 to solve for your x values.

x/2 = pi/3
x = 2pi/3

x/2 = 2pi/3
x = 4pi/3

Hope that helped!

~ ♥ ~

Answer 2

There's a little more to it because you ask for the general solution.

We have
x/2 = pi/3 + 2*pi*n where n is any integer, or
x/2 = 2pi/3 + 2*pi*n.

That's the general solution because it covers all possible answers, not just those between 0 and 2pi.

In the first case, we have

x = 2(pi/3 + 2*pi*n) = 2pi/3 + 4*pi*n

and for the second:

x = 2(2pi/3 + 2*pi*n) = 4pi/3 + 4*pi*n.

Answer 3

On a regular keyboard you can use sqrt(x). For other roots use x^(1/r).