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

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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

Mathematics
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If \(\sin \theta = -\frac{ 5 }{ 13 }, \pi<\theta<\frac{ 3\pi }{ 2 }\), find \(\cos \frac{ \theta }{ 2 }\). this?
haha yes!
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.

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Where are you suppose to use the sin theta part then?
Θ is in the 3rd quadrant so cos Θ is negative, and you can use the pythagorean theorem/triples to find it
Right so its 5 12 13 triangle what would you use for the cos theta part?
yes
so cos Θ would be -12/13
make sense?
So then you would just solve after?
right
Alright lets see how this works working it out then I might show you the work to see if its correct lol
@peachpi Like this?
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
Alright yeah its negative sorry its hard to tell but we got sqrt of 1 over 26?
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)
or -(√26)/26 if you have to rationalize
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?
that's a restriction on Θ. That's how we know Θ is in the 3rd quadrant.|dw:1436551969316:dw|
the question is asking for cos (Θ/2), not Θ itself
The answer is simple, A true saiyan sprinkles when he tinkles.
Wait so whats the answer then? im so confused lmaoo
I just said it
cos (Θ/2) = -√(1/26)
Is there a way to check the answer itself?
try wolframalpha.com not sure how you'd have to word it though
But are you sure your right? with the answer and everything?
yes
Alright I have an exam coming up which is why I am asking these questins XD haha thank you!
you're welcome

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