csc[tan-1(-0.62)]

The inverse tangent of a negative number is a negative angle
in the fourth quadrant.  The cosecant of an angle in the fourth 
quadrant is negative.  So the answer will be negative.

Let ϴ = tan-1(-0.62)

Then  

csc[tan-1(-0.62)] = csc(ϴ) 

So we want csc(ϴ)

tan(ϴ) = -0.62 =  = 

cot(ϴ) =  = 

We use 

csc²(ϴ) = 1 + cot²(ϴ) 

csc²(ϴ) = 1 + 

csc²(ϴ) = 1 + 

csc²(ϴ) =  + 

csc²(ϴ) = 

Take square roots of both sides.  And since we know
the answer is negative, we take the negative square root:

 csc(ϴ) = 

 csc(ϴ) = 

Edwin