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1. What is the domain of validity for csc theta=1/sin theta? A. All real numbers B. All real numbers except odd multiples of pi/2 C. All real numbers except even multiples of pi/2 D. All real numbers except multiples of pi

Sagot :

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[tex]\csc\Theta=\frac{1}{\sin\Theta}[/tex]

Since the function [tex]\csc\Theta[/tex] is literally defined as the reciprocal of [tex]\sin\Theta[/tex], any value of [tex]\Theta[/tex] will satisfy this equation.

A. All real numbers
[tex]\{\Theta|\Theta\in\mathbb{R}\}[/tex]

Answer:

Option D. All real numbers except multiples of pi

Step-by-step explanation:

It has been given that [tex]csc(\theta)=\frac{1}{sin\theta }[/tex] and we have to find the domain of the given expression.

As we know [tex]\frac{1}{sin\theta }[/tex] is defined only when [tex]sin\theta>0[/tex] or [tex]sin\theta<0[/tex] but not equal to zero.

Since sine of [tex]0, \pi, 2\pi......[/tex] are always zero. Therefore domain of [tex]\frac{1}{sin\theta }[/tex] is [tex]{\theta}<\pi or {\theta}>\pi[/tex]

That means Option D. All real numbers except multiples of pi is the answer.

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