To find the remaining trigonometric functions for angle a, we can use the given values of sin(a) and cos(a) and the Pythagorean identity:

sin^2(a) + cos^2(a) = 1

(1/7)^2 + (-6/7)^2 = 1
1/49 + 36/49 = 1
37/49 = 1

Now that we have sin(a) and cos(a) and know that sin^2(a) + cos^2(a) = 1, we can find the remaining trigonometric functions.

tan(a) = sin(a)/cos(a) = (1/7)/(-6/7) = -1/6

csc(a) = 1/sin(a) = 1/(1/7) = 7

sec(a) = 1/cos(a) = 1/(-6/7) = -7/6

cot(a) = 1/tan(a) = 1/(-1/6) = -6

Therefore, the remaining trigonometric functions for angle a are:
tan(a) = -1/6
csc(a) = 7
sec(a) = -7/6
cot(a) = -6