Final answer:
To find the values of the trigonometric functions of t, we can use the given information of sin(t) = 5/13 and cos(t) = -12/13. Using the Pythagorean identity sin^2(t) + cos^2(t) = 1, we can solve for sin(t). Then, we can use the definitions of the other trigonometric functions to find their values.
Step-by-step explanation:
To find the values of the trigonometric functions of t, we are given sin(t) = 5/13 and cos(t) = -12/13.
We can use the Pythagorean identity sin^2(t) + cos^2(t) = 1 to find the value of sin(t).
sin^2(t) + cos^2(t) = 1
(5/13)^2 + (-12/13)^2 = 1
25/169 + 144/169 = 1
169/169 = 1
Therefore, sin(t) = 5/13.
Now, we can use the definition of the other trigonometric functions to find their values. The tangent function is defined as tan(t) = sin(t)/cos(t), so tan(t) = (5/13)/(-12/13) = -5/12.
The other trigonometric functions can be found using the definitions: cos(t) = -12/13, sec(t) = 13/-12, csc(t) = 13/5, and cot(t) = -12/5.