Venice614
Answered

Welcome to Westonci.ca, where you can find answers to all your questions from a community of experienced professionals. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

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 :

RedRicin
[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.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.