What is the domain and range of $y = csc x$ $y=csc x$ ?

Question

What is the domain and range of $y = csc x$ $y=csc x$ ?

1 Answer

Impact of this question

34803 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-20T19:09:07

Domain of $y = csc (x)$ $y=csc(x)$ is $x\inRR, x\ne pi*n$ , $n\inZZ$ .
Range of $y=csc(x)$ is $y<=-1$ or $y>=1$ .

Explanation:

$y=csc(x)$ is the reciprocal of $y=sin(x)$ so its domain and range are related to sine's domain and range.

Since the range of $y=sin(x)$ is $-1<=y<=1$ we get that the range of $y=csc(x)$ is $y<=-1$ or $y>=1$ , which encompasses the reciprocal of every value in the range of sine.

The domain of $y=csc(x)$ is every value in the domain of sine with the exception of where $sin(x)=0$ , since the reciprocal of 0 is undefined. So we solve $sin(x)=0$ and get $x=0+pi*n$ where $n\inZZ$ . That means the domain of $y=csc(x)$ is $x\inRR, x\ne pi*n$ , $n\inZZ$ .

Science

Math

Humanities

... and beyond

What is the domain and range of $y = csc x$ $y=csc x$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

What is the domain and range of y=csc xy=cscxy=csc x?

1 Answer

Explanation:

Related questions

Impact of this question

What is the domain and range of $y = csc x$ $y=csc x$ ?