Question

The relationship 1/sin(θ) is equivalent to which of the following trigonometric functions?

A. cot(θ)
B. csc(θ)
C. arcsin(θ)
D. sec(θ)

Answer 1

`\bf sin(\theta)=\cfrac{1}{csc(\theta)} \qquad % cosine cos(\theta)=\cfrac{1}{sec(\theta)} \qquad % tangent tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)} \\\\\\ % cotangent cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad % cosecant \boxed{csc(\theta)=\cfrac{1}{sin(\theta)}} \qquad % secant sec(\theta)=\cfrac{1}{cos(\theta)}`

Answer 2

Option B is the correct answer.

Explanation:

We have the following trigonometric relations

`cosec\theta =(1)/(sin\theta )\\\\sec\theta =(1)/(cos\theta )\\\\cot\theta =(1)/(tan\theta )\\\\cot\theta =(cos\theta)/(sin\theta )\\\\tan\theta =(sin\theta)/(cos\theta )`

Here cosec θ is the correct answer.

Option B is the correct answer.