Venice614idn
Answered

Explore IDNLearn.com's extensive Q&A database and find the answers you're looking for. Ask your questions and receive reliable and comprehensive answers from our dedicated community of professionals.

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 :

RedRicinidn
[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.

We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Your search for answers ends at IDNLearn.com. Thank you for visiting, and we hope to assist you again soon.