Question

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

Answer 1

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?

Answer 2

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

Answer 3

Why can't you just use the point (0-1) amd move on from there? why is it infinity?

Answer 4

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

Answer 5

oh okay :D