Question

question 20 (1 point)
which of the following sets is the set of reciprocal trigonometric ratios?
o a) sec 0, cos 0, and cot 0
o b) sec 0, csc 0, and tan 0
o c) sin 0, csc 0, and cot 0
o d) sec 0, csc 0, and cot 0

Explanation:

Step1: Recall reciprocal trigonometric ratios

The reciprocal of \(\sin\theta\) is \(\csc\theta\) (\(\csc\theta=\frac{1}{\sin\theta}\)), the reciprocal of \(\cos\theta\) is \(\sec\theta\) (\(\sec\theta = \frac{1}{\cos\theta}\)), and the reciprocal of \(\tan\theta\) is \(\cot\theta\) (\(\cot\theta=\frac{1}{\tan\theta}=\frac{\cos\theta}{\sin\theta}\)).

Step2: Analyze each option

• Option a: \(\sec\theta\) is the reciprocal of \(\cos\theta\), but \(\cot\theta\) is not the reciprocal of \(\cos\theta\).
• Option b: \(\tan\theta\) is not a reciprocal trigonometric ratio in the sense of being a basic reciprocal (the basic reciprocals are related to \(\sin\), \(\cos\), \(\tan\) directly as \(\csc\), \(\sec\), \(\cot\)).
• Option c: \(\sin\theta\) is not a reciprocal trigonometric ratio (its reciprocal is \(\csc\theta\)).
• Option d: \(\sec\theta=\frac{1}{\cos\theta}\), \(\csc\theta=\frac{1}{\sin\theta}\), \(\cot\theta=\frac{1}{\tan\theta}\)

Answer:

D. \(\sec\theta,\csc\theta,\) and \(\cot\theta\)