PRACTICE Questions
$\mathrm{Lesson}5.1$
1. i) For each triangle, state the reciprocal trigonometric ratios for angle $\theta$.
ii) Calculate the value of $\theta$ to the nearest degree.
a)
b)
c)

Step 1 ：$\text{Reciprocal trigonometric ratios are:}$

Step 2 ：$\text{Cosecant (csc)}=\frac{1}{\sin }$

Step 3 ：$\text{Secant (sec)}=\frac{1}{\cos }$

Step 4 ：$\text{Cotangent (cot)}=\frac{1}{\tan }$

Step 5 ：$\text{a) Triangle with sides 3, 4, 5:}$

Step 6 ：$\text{Reciprocal trigonometric ratios:}$ $\text{csc}(\theta )=\frac{5}{3}$, $\text{sec}(\theta )=\frac{5}{4}$, $\text{cot}(\theta )=\frac{4}{3}$

Step 7 ：$\boxed{{\displaystyle \theta \approx {37}^{\circ }}}$

Step 8 ：$\text{b) Triangle with sides 5, 12, 13:}$

Step 9 ：$\text{Reciprocal trigonometric ratios:}$ $\text{csc}(\theta )=\frac{13}{5}$, $\text{sec}(\theta )=\frac{13}{12}$, $\text{cot}(\theta )=\frac{12}{5}$

Step 10 ：$\boxed{{\displaystyle \theta \approx {23}^{\circ }}}$

Step 11 ：$\text{c) Triangle with sides 8, 15, 17:}$

Step 12 ：$\text{Reciprocal trigonometric ratios:}$ $\text{csc}(\theta )=\frac{17}{8}$, $\text{sec}(\theta )=\frac{17}{15}$, $\text{cot}(\theta )=\frac{15}{8}$

Step 13 ：$\boxed{{\displaystyle \theta \approx {28}^{\circ }}}$