Find the trigonometric functions, if possible, of Sec 3pi/2

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Find the trigonometric functions, if possible, of Sec 3pi/2

Mathematics
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So, I was told that sin and cosine cannot both be equal to zero, which is obvious. Based on the unit circle's point, (0,-1) you can find the cosine easily. However, my teacher keeps telling me that the answer is wrong, can someone explain?
sec 3 pi/2 sec x= 1 / cos x sec (3* pi/2)= sec (pi+pi/2)=-sec pi/2= - infinity so cos 3pi/2= 0 sin 3 pi/2= -1 tan 3pi/2 = tan (pi+ pi/2)= tan pi/2 = infinity
Why can't you just use the point (0-1) amd move on from there? why is it infinity?

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it's infinity because cos x =0 so 1/ cos x= -infinity ( because cos and sec are negative in third quadrant)
oh okay :D

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