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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

User Smorka
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2 Answers

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\csc\Theta=(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}\}
User Matias Faure
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0 votes

Answer:

Option D. All real numbers except multiples of pi

Explanation:

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

As we know
(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
(1)/(sin\theta ) is
{\theta}<\pi or {\theta}>\pi

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

User Kyletaylored
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8.7k points
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