Question

acute angle w has sin w = 2 / √85 and sec w = 9 / √85. which are values of csc w and cos w?
o csc w = 9 / 2 and cos w = √85 / 9
o csc w = √85 / 2 and cos w = √85 / 9
o csc w = √85 / 2 and cos w = 2 / √85
o csc w = 9 / 2 and cos w = 2 / √85

Explanation:

Step1: Recall the reciprocal - relationship of sine and cosecant

We know that $\csc W=\frac{1}{\sin W}$. Given $\sin W = \frac{2}{\sqrt{85}}$, then $\csc W=\frac{\sqrt{85}}{2}$.

Step2: Recall the relationship between secant and cosine and use the Pythagorean identity

We know that $\sec W=\frac{\sqrt{85}}{9}$, and $\sec W=\frac{1}{\cos W}$, so $\cos W=\frac{9}{\sqrt{85}}$.

Answer:

$\csc W=\frac{\sqrt{85}}{2}$ and $\cos W=\frac{9}{\sqrt{85}}$