Given sinx=-4/5 and x is in quadrant 3, What is the value of tan x/2?

I have an answer but I'm not sure it's right...

Question

Given sinx=-4/5 and x is in quadrant 3, What is the value of tan x/2?

I have an answer but I'm not sure it's right...

anonymous · Answer

@hartnn Do you know?

hartnn · Answer

first find cos x from, 
$\sin^2 x +\cos^2x = 1$
sin x = -4/5 is given...

anonymous · Answer

I think the answer is -2 because it's in the 3rd quadrant...

hartnn · Answer

in 3rd quadrant, tan ratio is positive!

anonymous · Answer

Oh yea sorry! I meant 2.

hartnn · Answer

how u got 2 ?

hartnn · Answer

clarification required, 
is it tan (x/2) or (tan x) /2 ??

anonymous · Answer

$$\tan(\frac{ x }{ 2 })= \sqrt{\frac{ 1-cosx }{ 1+cosx }}$$

anonymous · Answer

$$\pm \sqrt{\frac{ 1-(\frac{ -3 }{ 5 }) }{ 1+\frac{ -3 }{ 5 } }}$$

hartnn · Answer

yes, correct!
from that you will select +2 because tan is +ve in 3rd quadrant...

anonymous · Answer

Thank you!

hartnn · Answer

ok, i got that you solved correctly :)
welcome ^_^

anonymous · Answer

It was wrong! It's -2!

hartnn · Answer

:O 
we missed a point!

hartnn · Answer

x is in quadrant 3, 
so, (x/2) will be in quadrant 2 !!
and tan is negative in quadrant 2....
silly mistake :(

hartnn · Answer

sorry!

anonymous · Answer

It's ok... :(