If cscx=3, 90 degrees

Question

If cscx=3, 90 degrees <x< 180 degrees then,
What is 
sin(x/2)=?
cos(x/2)=?
tan(x/2)=?
I know I have to use double angle formulas but I'm a bit confused, can someone please help ?

yttrium · Answer

Where you get stucked?

anonymous · Answer

The fact that I'm working with csc and that's (x/2), so I don't understand the problem

yttrium · Answer

But can you solve the sinx, cosx,and tanx of this?

yttrium · Answer

When you already solved that, that is the time you can solve for the problem itself using half-angle identities. :) Do you know it?

anonymous · Answer

Yeah I just have trouble starting it

yttrium · Answer

Let's get started.
$$cscx = \frac{ hyp }{opp } = \frac{ 3 }{ 1 }$$
Therefore, hypotenuse is equal to 3 and the side opposite is equal to 1. So, by pythagorean theorem you can solve the 3rd side. Using pythagorean theorem, we can solve the  the adj side So what is the value of the 3rd side?.

anonymous · Answer

2sqrt(2)

yttrium · Answer

I think it would be better if you @dnova21  will join me solving so you can as well visualise what's happening during solving. :))

anonymous · Answer

|dw:1382164602788:dw| now find cos x and tanx and find sinx/2 and others

anonymous · Answer

so if I found that cscx=2sqrt(2) then I can just follow what Harindu mentioned ?

yttrium · Answer

No.cscx = 3 and not 2sqrt2.
2sqrt2 is actually the value of our adjacent side. Actually it is -2sqrt(2) since the problem tells us that is is found on the 2nd quadrant.

anonymous · Answer

Oh okay

anonymous · Answer

lol since sinx and cosx between 90 and 180 are postive and cos and tangen are negative

yttrium · Answer

So, given the triangle |dw:1382166441051:dw|
What are the sinx, cosx and tanx of our angle?

@Harindu , we actually used here the coordinate plane as well. Such angle found bet 90 and 180 are found in quadrant two and hence all values of x must be negative.