Question

How do you plug the inverse csc (-7/3) into the calculator?

Answer 1

Use the inverse sine function.

Explanation:

`csc^-1(-7/3)` is a number between `-pi/2` and `pi/2` whose cosecant is `-7/3`).

That means the sine is `-3/7`.

`csc^-1(-7/3) = sin^-1(-3/7)`.

In general,
because `csc theta = 1/sin theta`,

we have: `csc^-1 x = sin^-1 (1/x)`

Note: we use a similar idea to find inverse secant and inverse cotangent on many calculators.

`sec^-1 x = cos^-1(1/x)`

and

`cot^-1 x = tan^-1(1/x)`

(The last works if we take the range of `cot^-1` to be the same as that of `tan^-1` -- a popular choice in this computer age.
The description is a bit more complicated if we take the range of `cot^-1 x` to be the same as that of `cos^-1` -- a traditional choice that makes the inverse cotangent continuous.)

Answer 2

Plug in calculator to find csc(-7/3)

Ans: arc x = -25.37 deg

Explanation:

Order of plug in:

(7) (:) (3) (=) (-) (1/x) (2nd) (sin)

The answer will be `x = - 25.37` deg