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!