Question

If cot x = -4/3 find csc x, if 270°<x<360"​

Answer 1

csc x = -
`(5)/(3)`

Explanation:

Using the trigonometric identity

csc²x = 1 + cot²x

= 1 + (-
`(4)/(3)` )² = 1 +
`(16)/(9)` =
`(25)/(9)`, thus

csc x = ±
`\sqrt{(25)/(9) }` = ±
`(5)/(3)`

Since 270° < x < 360° where csc x < 0 , then

csc x = -
`(5)/(3)`