The domain of y=csc(x) is all real numbers except the values [tex]\pi n[/tex] for all integers [tex]n[/tex].
Explanation:
The domain of the function [tex]y=csc(x)=\frac{1}{sin(x)}[/tex] is all real numbers except the values where [tex]sin(x)[/tex] is equal to [tex]0[/tex] , that is, the values [tex]\pi n[/tex] for all integers [tex]n[/tex]. The range of the function is y ≤ −1 or y ≥ 1 .
The cosecant (csc) angle is the length of the hypotenuse divided by the length of the opposite side. the inverse of [tex]csc[/tex]is [tex]arccsc[/tex]. The cosecant of x is defined to be 1 divided by the sine of x: [tex]csc (x) =[/tex] [tex]\frac{1}{ sin x}[/tex]
[tex]y=csc(x)[/tex] is the reciprocal of [tex]y=sin(x)[/tex], therefore its domain and range are related to sine's domain and range.
Because the range of [tex]y=sin(x)[/tex] is −1≤y≤1 so thst the range of [tex]y=csc(x)[/tex] is y
≤
−
1 or y
≥
1
, which surround the reciprocal of every value in the sine range
The domain of [tex]y=csc(x)[/tex] is every value in the domain of sine with the exception of where [tex]sin(x)=0[/tex]
, because the reciprocal of [tex]0[/tex] is undefined.
Then we solve [tex]sin(x)=0[/tex] and get [tex]x=0+\pi n[/tex] where n ∈ Z
. That means the domain of [tex]y=csc(x)[/tex] is x ∈ R
, [tex]x \neq \pi n[/tex]
, n
∈
Z
.
Learn more about the domain of y = csc(x) https://brainly.com/question/14028117
#LearnWithBrainly
