PLEASE HELP!!!

If sin(x)=1/2 and pi/2

Question

PLEASE HELP!!!

If sin(x)=1/2 and pi/2 <x<pi, find cos(x) and hence find tan(x)

Please explain me how!

anonymous · Answer

$$-\sqrt3/2$$

zehanz · Answer

If you haven't learned this already by heart (joking), you can do the following:

use sin²x+cos²x=1 to go from sin to cos: cos²x=1-sin²x.

This leaves you with one problem: there are 2 possible values for cos x: + or - the sqrt of 1-sin²x.

Which one is it? 
The answer lies in: pi/2 <x<pi, because from this you can determine whether cos is + or -.

Once you've got sin and cos, finding tan x is easy!

zehanz · Answer

@cahit: just giving an answer won't help much...

anonymous · Answer

then $$-1/\sqrt3$$

anonymous · Answer

the previous answer was for cosx, and the secand one for tanx

anonymous · Answer

@ZeHanz  I LOVE THE METHOD! THANK YOU SO MUCH :)
@cahit THANK YOU !!

zehanz · Answer

YW!

zehanz · Answer

Together, we're quite a team, @cahit and me ;)

anonymous · Answer

haha i am so glad such a team like you guys helped me  :))