Answer:
csc x = - [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
Using the trigonometric identity
csc²x = 1 + cot²x
= 1 + (- [tex]\frac{4}{3}[/tex] )² = 1 + [tex]\frac{16}{9}[/tex] = [tex]\frac{25}{9}[/tex], thus
csc x = ± [tex]\sqrt{\frac{25}{9} }[/tex] = ± [tex]\frac{5}{3}[/tex]
Since 270° < x < 360° where csc x < 0 , then
csc x = - [tex]\frac{5}{3}[/tex]
