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Cosine theta=8/17 and 270 degrees is < theta, and theta is< 360

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θ is in QIV, so x>0 and y<0

cosθ = x/r = 8/17

so,

x = 8
y = -15
r = 17

Now recall the other trig functions:
sinθ = y/r
tanθ = y/x

Sin= -15/17
Cos= 8/17
Tan= -15/8
Csc=-17/15
Sec= 17/8
Cot= -8/15

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