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

Question

#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)=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