Quick help?!?!?

Question

evaluate tan(arccsc-1)

please show work

Answer 1

Arcsec(-1) is the same angle where its reciprocal function (sine) is also -1, which is 3π/2.

tan (arcsec(-1)) =

tan(3π/2)=

undefined

(since tanΘ = sinΘ / cosΘ, and cosΘ = 0)

Answer 2

First, what angle gives us a cosecant value of -1? Well this would be the same angle where we get a sine value of -1, which occurs at 3π/2. So now that you have the angle represented by arccsc(-1), what is tan(3π/2)? sin(3π/2) = -1 and cos(3π/2) = 0, so since tan(x) = sin(x)/cos(x), we get tan(3π/2) approaches something of the form -1/0. We can't divide by zero, so the tangent value is undefined.

tan(arccsc(-1)) is undefined.

Answer 3

Princile value:

csc θ = -1

θ = 3π / 2

tan (3π / 2) = ?