How do you evaluate the expression #csc(-45)#?

1 Answer
Jul 22, 2018

#-sqrt2#

Explanation:

Recall that

#csctheta=1/sintheta# and #sin(-theta)=-sin(theta)#

With this in mind, we can rewrite our expression as

#1/sin(-45)#, which is the same as #1/-sin(45)#

The Unit Circle coordinates for #45^@# are #(sqrt2/2,sqrt2/2)# where the #y#-coordinate is the #sin# value. We now have

#1/-(sqrt2/2)#

Which can be rewritten as

#-2/sqrt2#, and rationalized as #-sqrt2#

Hope this helps!