If sin theta = 1/3, theta in quadrant 2, find the exact value of
cos theta
sin(theta+pi/6)
cos(theta-pi/3)
tan(theta+pi/4)

So hmm checking the picture below

you can pretty much just use the pythagorean theorem to get the missing adjacent side

once you have that, you just get the cosine since the cosine is just adjacent/hypotenuse

as far as the sum with θ, those angles would be in your Unit Circle surely
and just expand the sum identity with those values

The answer of the above is

P(chicago, illinois)