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

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

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Answer 1 · 2015-07-28T17:29:59

Use the inverse sine function.

Explanation:

${csc}^{- 1} (- \frac{7}{3})$ $csc^-1(-7/3)$ is a number between $- \frac{π}{2}$ $-pi/2$ and $\frac{π}{2}$ $pi/2$ whose cosecant is $- \frac{7}{3}$ $-7/3$ ).

That means the sine is $- \frac{3}{7}$ $-3/7$ .

${csc}^{- 1} (- \frac{7}{3}) = {sin}^{- 1} (- \frac{3}{7})$ $csc^-1(-7/3) = sin^-1(-3/7)$ .

In general,
because $csc θ = \frac{1}{sin θ}$ $csc theta = 1/sin theta$ ,

we have: ${csc}^{- 1} x = {sin}^{- 1} (\frac{1}{x})$ $csc^-1 x = sin^-1 (1/x)$

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

${sec}^{- 1} x = {cos}^{- 1} (\frac{1}{x})$ $sec^-1 x = cos^-1(1/x)$

and

${cot}^{- 1} x = {tan}^{- 1} (\frac{1}{x})$ $cot^-1 x = tan^-1(1/x)$

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

Answer 2 · 2015-07-28T19:16:03

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 $x = - 25.37$ $x = - 25.37$ deg

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

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