Question 841711
The angle must be located in the 2nd quadrant.  In the second quadrant:  sin and csc are positive, while cos, sec, tan, and cot are negative.<P>
tan(t) = 8.  tan = opp/adj.  Pick any numbers for opp/adj such that the quotient is 8.  Don't worry about the sign of your answers.  The quadrant (2nd) tells you the sign of each of the functions.<P>
tan(t)= 8 = 8/1.  Opposite side is 8, adjacent side is 1.  The hypotenuse is {{{sqrt(8^2 + 1^2) = sqrt(65)}}}<P>
Now you can find all of the requested values.  Remember, only sin and csc are positive:<P>
sin(t) = opp/hyp = {{{8/sqrt(65)}}} = approximately .992<P>
csc(t) = 1/(sin(t) = 1/.992 = approximately 1.008<P>
cos(t) = adj/hyp = {{{1/sqrt(65)}}} = appox. -.124.  Remember, cos is negative in the second quadrant.  Don't worry about the sign, until you complete the calculation.  Then add the sign based on the quadrant.  
sec(t) = 1/cos(t) = 1/(-.124) = appox. -8.062.<P>
tan(t) is already given:  -8.  cot(t) is 1/tan(t) = -1/8