Evaluate the following expression, using a calculator if necessary. If the answer does not exist, indicate "DNE." ${csc}^{- 1} (- .01)$ $csc^-1(-.01)$ Enter your answer in radians rounded to four decimal places?

Question

${csc}^{- 1} (- .01)$ $csc^-1(-.01)$

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Answer 1 · 2018-04-06T15:05:35

DNE

This is the arc cosecant function.

You calculator is unlikely to have a key for this function.

We can use instead the fact that:

$csc (x) = \frac{1}{sin (x)}$ $csc(x)=1/sin(x)$

$:.$

$1/sin(x)=-0.01$

$sin(x)=-1/0.01$

$x=sin^-1(sin(x))=sin^-1(1/0.01)$

So we use:

$sin^-1(-1/0.01)$

We can see without using a calculator, that:

$|-1/0.01|>1$

The sine ratio for real numbers is always in the interval:

$-1<=sin(x)<=1$

or:

$|sin(x)|<=1$

This means there are no real number solutions to this.

DNE