Question

final exam (precalculus)
score: 20/25 answered: 20/25
question 21
for each part, type your answer in as a fraction. do not use a decimal or round your answers.
if sin(x) = 3/5, then csc(x) =
if cos(x) = 2/3, then sec(x) =
if tan(x) = 7, then cot(x) =

Explanation:

Step1: Recall reciprocal identities

$\csc(x)=\frac{1}{\sin(x)}$, $\sec(x)=\frac{1}{\cos(x)}$, $\cot(x)=\frac{1}{\tan(x)}$.

Step2: Calculate $\csc(x)$

Given $\sin(x)=\frac{3}{5}$, then $\csc(x)=\frac{1}{\frac{3}{5}}=\frac{5}{3}$.

Step3: Calculate $\sec(x)$

Given $\cos(x)=\frac{2}{3}$, then $\sec(x)=\frac{1}{\frac{2}{3}}=\frac{3}{2}$.

Step4: Calculate $\cot(x)$

Given $\tan(x) = 7$, then $\cot(x)=\frac{1}{7}$.

Answer:

$\frac{5}{3}$
$\frac{3}{2}$
$\frac{1}{7}$