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

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Answer 1 · 2018-07-22T15:50:06

#-sqrt2#

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!