Question

If csc x = −5, find csc(−x) find the period and horizontal shift

Answer 1

`\csc (-x) = - \csc x = - ( - 5) = 5`

Period is 2π

Horizontal shift = 0

Explanation:

We know that
`\sin (-x) = - \sin x` and as
`\csc x = (1)/(\sin x)`, so, we can write
`\csc (-x) = - \csc x`

Therefore, the if
`\csc x = - 5` then
`\csc (-x) = - \csc x = - ( - 5) = 5` (Answer)

Now, the period of
`\csc x` is 2π, hence the period of
`\csc (- x)` is also 2π. (Answer)

Again.
`\csc ( - x) = \csc (-x + 0)`, hence, the horizontal shift of
`\csc (- x)` is 0. (Answer)