Evaluate the following expression, using a calculator if necessary. If the answer does not exist, indicate "DNE." csc^-1(-.01)csc1(.01) Enter your answer in radians rounded to four decimal places?

csc^-1(-.01)csc1(.01)

1 Answer
Apr 6, 2018

DNE

Explanation:

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)csc(x)=1sin(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