PRACTICE Questions
$\operatorname{Lesson} 5.1$
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 ：\(\boxed{\theta \approx 37^\circ}\)

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 ：\(\boxed{\theta \approx 23^\circ}\)

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 ：\(\boxed{\theta \approx 28^\circ}\)