Question 1094889
<pre>
Draw a right triangle in quadrant IV,

Since the sine is opposite/hypotenuse, label the opposite
side as the numerator of {{{-5/8}}}, which is -5, and
the hypotenuse as +8. Then use the Pythagorean theorem
to find the length of the adjacent side {{{sqrt(39)}}}.

{{{drawing(400,400,-7,7,-7,7,
red(arc(0,0,2.7,-2.7,0,322)),
line(-10,0,10,0), line(0,-10,0,10), locate(3,-2.5,8),
locate(3.1,.6,sqrt(39)),locate(6.4,-2.5,-5),
triangle(0,0,sqrt(39),0,sqrt(39),-5)  )}}}

{{{sec(theta)=hypotenuse/adjacent = 8/sqrt(39)=8sqrt(39)/39}}}

{{{cot(theta)=adjacent/opposite=-5/sqrt(39)=-5sqrt(39)/39}}}

Edwin</pre>