Answer:
[tex]\csc(270 \degree)}=-1[/tex]
Step-by-step explanation:
We want to find the value of [tex]\csc(270\degree)[/tex].
Recall from the reciprocals of trigonometric ratios that;
[tex]\csc(270\degree)=\frac{1}{\sin 270\degree}[/tex]
Note that; 270 degrees is a quadrantal angle. It makes an angle of 90 degrees with the positive x-axis and it is in the third quadrant
This implies that;
[tex]\csc(270 \degree)=- \csc(90 \degree)[/tex]
[tex]\csc(270 \degree)=\frac{1}{-\sin 90\degree}[/tex]
[tex]\csc(270 \degree)=-\frac{1}{\sin 90\degree}[/tex]
On the unit circle, [tex]\sin(90\degree)=1[/tex]
This implies that;
[tex]\csc(270\degree)=-\frac{1}{1}=-1[/tex]
