Acute angle W has sin W and sec W= sqrt/9. Which are values of csc W and cos W?

Answer 1

Given that sec W = sqrt(9), we can find cos W by using the identity sec^2 = 1 + tan^2:

sec^2 W = 1 + tan^2 W

(sqrt(9))^2 = 1 + tan^2 W

9 = 1 + tan^2 W

tan^2 W = 8

tan W = sqrt(8)

Now we can find csc W using the identity csc^2 = 1 + cot^2:

sin^2 W = 1 - cos^2 W
sin^2 W = 1 - (9/9)
sin^2 W = 0
sin W = 0

csc W = 1/sin W
csc W = 1/0
csc W is undefined because sin W is zero.