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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

Verified Answer :

RedRicin

\(\csc\Theta=\frac{1}{\sin\Theta}\)

Since the function \(\csc\Theta\) is literally defined as the reciprocal of \(\sin\Theta\), any value of \(\Theta\) will satisfy this equation.

A. All real numbers
\(\{\Theta|\Theta\in\mathbb{R}\}\)

Answer:

Option D. All real numbers except multiples of pi

Step-by-step explanation:

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

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

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

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

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