Question

Find the exact value of csc (-4pi/3)

1. 2sqrt3/3
2. sqrt3/2
3. -sqrt3/2
4. -2sqrt3/3

Answer 1

option 1

2sqrt3/3

Explanation:

Given in the question

csc(-4π/3)

we know that csc(x) =
`(1)/(sin(x))` that means

`csc((-4\pi)/(3))=(1)/(sin((-4\pi)/(3) ))`

sin(-4π/3) =
`(√(3))/(2)`

so,

`csc((-4\pi)/(3))=(1)/((√(3))/(2) )`

`(1)/(√(3)/2 )` =
`(2)/(√(3))=(2√(3))/(3)`