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@phi or @jim_thompson5910 or @zepdrix
can anyone of you explain this to me please. thank you so much

Sine positive, cosine negative, so we're in the 2nd quadrant.

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how was the cosine negative?

cos(s) < 0 was in the problems description. Less than zero means it's negative :)

Lots of little details to this problem, it's easy to miss stuff :D heh

So hmm, let's try to solve for t.

okay

pi/3 is the 60 degree

So in the 4th quadrant is it, 5pi/3 maybe?

aw :D

yes its 5pi/3

i checked by drawing haha

ah good :)

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by doing it the same way? but wouldnt we get....hm...the same 12 and 13?

\[\large \cos(s-t)=\cos(s)\cos(t)+\sin(s)\sin(t)\]

This is a pretty rough problem :D I don't remember doing anything like this in trig lol

haha, dang...okay hmmm.. okay so i just plug in right? . lol

So looking at our triangle we drew on the coordinate plane, can you determine cos(s)?

well the cos s. would be the path. the. that equaled 5, right?

Cosine would be Adjacent over Hypotenuse, soh cah toa :D CAH! C=A/H

If this had been the UNIT circle, then yes you would be correct :)

lol ya, so 5 right? wait.....lol hold on

Look at the triangle.
The Hypotenuse is ummm 13 I think.

i got 12/13=.923

woops you calculated sin again :O

12 is the side OPPOSITE s.

what/! haha hold on

okay i got 13/12 = 1.0833

5 is the side ADJACENT to s.
13 is the HYPOTENUSE :D
silly sis ^^

Keep in mind we're going to leave it as a FRACTION, they want an EXACT answer.

okay

so 5/13 = .3846

Ok cool c:

Ah crap I just noticed, the cosine should be a NEGATIVE value, remember why?

because its in the 3rd quad?

AH! I means 2nd

lol ya c: because of that.

now you have to think back to your special angles.
What do you get for sin(t) and cos(t)? :o

crud, i forgot the special angles :/ okay um...sin t would be.... - 1/2 ?

oh man :? im so bad at this haha your right

lol :D

the cos is going to be 1/2 then

K sounds good :D positive right? since we're in the 4th.

yes. but how did we get from 2nd to fourth? haha i just noticed that

Oh S was in 2nd :) t was in 4th

They're making us jump around and use 2 different angles.

WAIT! i see it, tan t is - sqrt 3, so that means -sin/+ cos haha okay 4th Q

oh...thats true

okay so now i solve that equation?? or do we gotta get another anser?

haha okay hold on let me try it

i got - 5/12, haha and i cant do the other one

OH! -5/26 sorry haha

Sounds like you're on the right track though :D

dang. haha thank you so much

just let me know when you have to get off okay :)

okay :)

fyi,
you got the exact answer
\[ \cos(s-t)= \frac{-(5+12\sqrt{3})}{26} \]