question 20 (1 point)\nwhich of the following sets is the set of reciprocal trigonometric ratios?\no a) sec…

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)