Question 708067
<pre>
csc[tan<sup>-1</sup>(-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 &#1012; = tan<sup>-1</sup>(-0.62)

Then  

csc[tan<sup>-1</sup>(-0.62)] = csc(&#1012;) 

So we want csc(&#1012;)

tan(&#1012;) = -0.62 = {{{-62/100}}} = {{{-31/50}}}

cot(&#1012;) = {{{1/tan(theta)}}} = {{{-50/31}}}

We use 

cscē(&#1012;) = 1 + cotē(&#1012;) 

cscē(&#1012;) = 1 + {{{(-50/31)^2}}}

cscē(&#1012;) = 1 + {{{2500/961}}}

cscē(&#1012;) = {{{961/961}}} + {{{2500/961}}}

cscē(&#1012;) = {{{3461/961}}}

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

 csc(&#1012;) = {{{-sqrt(3461/961)}}}

 csc(&#1012;) = {{{-sqrt(3461)/31)}}}

Edwin</pre>