Answer: Cosecant is undefined at 180°.
Step-by-step explanation:
Since we have given that
Cosecant i.e. cosec Θ
Since we know from the "trigonometric table"
If Θ = 45°
[tex]cosec\ 45^\circ=\sqrt{2}[/tex]
so, cosecant is defined.
If Θ = 60°,
[tex]cosec\ \theta=\frac{2}{\sqrt{3}}[/tex]
So, cosecant is defined again.
If Θ = 180°
[tex]cosec\ (180^\circ)=-cosec\ 0^\circ=\infty[/tex]
So, it is not defined.
If Θ = 270°
then [tex]cosec\ 270^\circ=(-)cosec\ 90^\circ=-1[/tex]
so, it is defined.
Hence, cosecant is undefined at 180°.
