What is the exact value of csc75Ï€? Also is the value of cos(5Ï€/2) equal to 0?

Question

For csc75π, you go around and around the circle..and then end up at (-1,0). For csc, you get the value by dividing the radian value (1) by the y-value (0). But you can't divide 1 by 0! Arrgh, I'm confused. Am i wrong in my logic? If so, explain. If not, what do I write? Undefined? *sigh* Also, for cos(5π/2), can a trigonometric function be 0?

Answer 1

csc75π

get in in range 0 to 2pi

csc75π = cscπ ( mod 2π)

as sin π = 0 so cscπ = infininite

your approach is right.

cos (5pi/2) = - 1/sqrt(2) and not zero

cos  

Answer 2

alright now csc(75pi) is same as 1/sin(75pi) =  approximately -2 X 10^11. Now for cos(5pi/2) it is always going to be zero. and yes a trigonomic funcation can be zero.