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.

tan(t)= 8 = 8/1. Opposite side is 8, adjacent side is 1. The hypotenuse is

Now you can find all of the requested values. Remember, only sin and csc are positive:

sin(t) = opp/hyp = = approximately .992

csc(t) = 1/(sin(t) = 1/.992 = approximately 1.008

cos(t) = adj/hyp = = 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.

tan(t) is already given: -8. cot(t) is 1/tan(t) = -1/8
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Find the values of the trigonometric functions of t from the given information.
Given data shows reference angle t is in quadrant II where sin>0, cos<0, tan<0.
Hypotenuse of reference right triangle=√(8^2+1^2)=√(64+1)=√65
tan t= −8, csc t > 0
sin t=8/√65=8√65/65
cos t=-1/√65=-√65/65
tan t=-8
sec t=-√65
csc t=√65/8
cot t=-1/8