Question

How do you find the general solutions for `csc4x=2`?

Answer 1

Solve `csc (4x) = 2`

Ans: `pi/24` and `(5pi)/24`

Explanation:

`csc (4x) = 1/(sin 4x) = 2` --> `sin 4x = 1/2`

Trig Table of Special Arcs gives:
`sin 4x = 1/2` --> `4x = pi/6` and `4x = 5pi/6`

a. `4x = pi/6` --> `x = pi/24`
b. `4x = (5pi)/6` --> `x = (5pi)/24`