Question

For which of the following angles is cosecant undefined? 45° 60° 180° 270°

Answer 1

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°

$cosec\ 45^\circ=\sqrt{2}$

so, cosecant is defined.

If Θ = 60°,

$cosec\ \theta=\frac{2}{\sqrt{3}}$

So, cosecant is defined again.

If Θ = 180°

$cosec\ (180^\circ)=-cosec\ 0^\circ=\infty$

So, it is not defined.

If Θ = 270°

then $cosec\ 270^\circ=(-)cosec\ 90^\circ=-1$

so, it is defined.

Hence, cosecant is undefined at 180°.

Answer 2

Cosecant = 1/sin so it is where sin =0. Out of these sin is 0 at 180 degrees