if sin theta equals -5/13 pi is less than theta less than 3 pi/2 find cos theta over 2

This is just all over the place

Question

if sin theta equals -5/13 pi is less than theta less than 3 pi/2 find cos theta over 2

This is just all over the place

anonymous · Answer

If $\sin \theta = -\frac{ 5 }{ 13 }, \pi<\theta<\frac{ 3\pi }{ 2 }$, find $\cos \frac{ \theta }{ 2 }$.

this?

anonymous · Answer

haha yes!

anonymous · Answer

you need to use the half angle identity
$$\cos \theta = \pm \sqrt{\frac{ 1+\cos \theta }{ 2}}$$
which means you need to find cos Θ.

anonymous · Answer

Where are you suppose to use the sin theta part then?

anonymous · Answer

Θ is in the 3rd quadrant so cos Θ is negative, and you can use the pythagorean theorem/triples to find it

anonymous · Answer

Right so its 5 12 13 triangle what would you use for the cos theta part?

anonymous · Answer

yes

anonymous · Answer

so cos Θ would be -12/13

anonymous · Answer

make sense?

anonymous · Answer

So then you would just solve after?

anonymous · Answer

right

anonymous · Answer

Alright lets see how this works working it out then I might show you the work to see if its correct lol

anonymous · Answer

@peachpi Like this?

anonymous · Answer

I can't really see if the 12/13 is negative. If it is then you're right and you just have to simplify it

anonymous · Answer

Alright yeah its negative sorry its hard to tell but we got sqrt of 1 over 26?

anonymous · Answer

that's what I got. Then since Θ is in the third quadrant, Θ/2 is in the second where cos is negative so got with -√(1/26)

anonymous · Answer

or -(√26)/26 if you have to rationalize

anonymous · Answer

but I don't think either of them are right becauase the answer has to be greater then pi and less then 3 pi over 2?

anonymous · Answer

that's a restriction on Θ. That's how we know Θ is in the 3rd quadrant.|dw:1436551969316:dw|

anonymous · Answer

the question is asking for cos (Θ/2), not Θ itself

anonymous · Answer

The answer is simple, A true saiyan sprinkles when he tinkles.

anonymous · Answer

Wait so whats the answer then? im so confused lmaoo

anonymous · Answer

I just said it

anonymous · Answer

cos (Θ/2) = -√(1/26)

anonymous · Answer

Is there a way to check the answer itself?

anonymous · Answer

try wolframalpha.com
not sure how you'd have to word it though

anonymous · Answer

But are you sure your right? with the answer and everything?

anonymous · Answer

yes

anonymous · Answer

Alright I have an exam coming up which is why I am asking these questins XD haha thank you!

anonymous · Answer

you're welcome