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

Question

a) csc W =9/2 and cos W = 9/sqrt 85
b) csc W = sqrt 85/2 and cos W = 2/ sqrt 85
c) csc W = sqrt 85/2 and cos W = 9/ sqrt 85
d) csc W = 9/2 and cos W = 2/sqrt85

Answer 1

To find the values of csc W and cos W, we'll use the information given:

sec W = sqrt(9) = 3
sec W = 1/cos W
Therefore, cos W = 1/3.

Since sin^2 W + cos^2 W = 1, we can find sin W:
sin^2 W + 1/9 = 1
sin^2 W = 8/9
sin W = sqrt(8)/3

Now, csc W = 1/sin W = 1 / (sqrt(8)/3) = 3 / sqrt(8) = 3sqrt(8) / 8 = sqrt(72) / 8 = sqrt(9*8)/8 = sqrt(9) * sqrt(8) / 8 = 3sqrt(2) / 8

So, the values of csc W and cos W are:
c) csc W = sqrt(85) / 2 and cos W = 9 / sqrt(85)