Question

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

Answer 1

$\csc\Theta=\frac{1}{\sin\Theta}$

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 2

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 $sin\theta$ but not equal to zero.

Since sine of $0, \pi, 2\pi......$ are always zero. Therefore domain of $\frac{1}{sin\theta }$ is ${\theta}\pi$

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