Solving Angle X with Sin(x/2)=1/2 & Tan(x)=sqrt(3)

[Anzas]

find the angle x
if its known that:
sin(x/2) = 1/2
tan(x)=sqrt(3)

0<=x<=360

 

[Pyrrhus]

why don't you simply do arcsine and arctan?

 

[Anzas]

because the whole point of the question is using trigonometric identities to solve it (believe me i would be happy to do the arctan and get it over with )

 

[NateTG]

because the whole point of the question is using trigonometric identities to solve it (believe me i would be happy to do the arctan and get it over with )

You might discover something interesting about the problem though. (It's also worth noting that that there are special angles involved.)

 

[Anzas]

i tried playing around with it

sin(x/2) = 1/2
tan(x)=sqrt(3)

i got

tan(x) = sin(x) / cos(x) = sqrt(3)

sin^2(x) / cos^2(x) = 3

but that didn't really lead me anywhere
i thought of ways to convert sin(x/2) to sin(x) with no luck

 

[Tide]

find the angle x
if its known that:
sin(x/2) = 1/2
tan(x)=sqrt(3)

0<=x<=360

If you don't want to use the inverse trig functions directly then you may want to ponder the equilateral triangle!