Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. acute angle (w) has (sin w=\frac{4}{sqrt{97}}) and (\tan w = \frac{4}{9}). which are values of (csc w) and (cot w)? (csc w=\frac{sqrt{97}}{4}) and (cot w=\frac{9}{4}) (csc w=\frac{9}{sqrt{97}}) and (cot w=\frac{4}{sqrt{97}}) (csc w=\frac{sqrt{97}}{4}) and (cot w=\frac{4}{sqrt{97}}) (csc w=\frac{9}{sqrt{97}}) and (cot w=\frac{9}{4})

Explanation:

Step1: Recall reciprocal identities

Recall that $\csc W=\frac{1}{\sin W}$ and $\cot W = \frac{1}{\tan W}$.

Step2: Calculate $\csc W$

Given $\sin W=\frac{4}{\sqrt{97}}$, then $\csc W=\frac{1}{\sin W}=\frac{\sqrt{97}}{4}$.

Step3: Calculate $\cot W$

Given $\tan W=\frac{4}{9}$, then $\cot W=\frac{1}{\tan W}=\frac{9}{4}$.

Answer:

$\csc W=\frac{\sqrt{97}}{4}$ and $\cot W=\frac{9}{4}$, so the answer is $\csc W=\frac{\sqrt{97}}{4}$ and $\cot W=\frac{9}{4}$ (corresponding to the first - option).