Why is the output of my function infinity?

I'm doing code for the trapezoidal rule. I checked my code with simple functions at first to make sure it was outputting correctly. However when I am attempting what I need to do, my output says it's infinity, when it should not be. The solution I got from Wolfram Alpha and my TI89 was 0.00958. Could it be the "1/n" in the x definition? I needed 10 steps for the trapezoids I'm setting up.

The function being applied is: cos^2((pi*cos(x))/2)*csc(x).

n = 10;
x = 0:1/n:1/2;
y=cos((pi*cos(x))/2).^2.*csc(x);
z=trapz(x,y)

Answer 1

[Star Strider]

The cosecant is , so at integral multiples of π (such as 0, π, ...) the cosecant will approach ∞.

[Nicholas Gillam]

Whoops, your comment made me remember that I forget to specify that the limits of integration are from 0 to 1/2.

[Star Strider]

n = 10;
x = 0:1/n:1/2;

Your upper limit of integration changes nothing, unfortunately.

Note that is — and will likely always be — ∞.

[Nicholas Gillam]

Hmm, there must be something I can do to simplify it, especially if Wolfram Alpha and my TI89 are giving me a finite number.

[Star Strider]

Wolfram Alpha and your Ti89 are wrong.

Answer 2

[Torsten]

Since your function tends to 0 as x -> 0 by L'Hospital, you can integrate

y = cos((pi*cos(x))/2).^2.*csc(x).*(x > 0);