Question

Solve on the interval [0,2pi)
4 CSC x + 1 = -3

Answer 1

`$(3\pi )/(2)$`

Explanation:

Solve for the interval:
`[0, 2\pi)`

`4 \csc(\theta)+1=-3`

`4 \csc(\theta)=-4`

`\csc(\theta)=-1`

`$(1)/(\sin(\theta)) =-1 \Rightarrow \sin(\theta)=-1$`

We have
`\sin(\theta)=-1` for coterminal angles
`$(3\pi )/(2)+2\pi n$`

Once we just want the interval
`[0, 2\pi)`

The solution is
`$(3\pi )/(2)$`