Question

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

Answer 1

Answer:

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

Period is 2π

Horizontal shift = 0

Step-by-step explanation:

We know that $\sin (-x) = - \sin x$ and as $\csc x = \frac{1}{\sin x}$, 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)