Final answer:
To find the values of the remaining trigonometric functions, 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 find sin^2 t = 25/169 and cos^2 t = 144/169. With these values, we can calculate tan t, csc t, sec t, and cot t.
Step-by-step explanation:
To find the values of the remaining trigonometric functions at t, we can use the given information of sin t = 5/13 and cos t = -12/13. We can use the Pythagorean identity, which states that sin2t + cos2t = 1, to find the value of sin2t. Since we know that sin t = 5/13, we can square this value to get sin2t = (5/13)2 = 25/169. Similarly, we can square the value of cos t = -12/13 to get cos2t = (-12/13)2 = 144/169.
Using these values, we can now find the remaining trigonometric functions:
- tan t = sin t/cos t = (5/13)/(-12/13) = -5/12
- csc t = 1/sin t = 1/(5/13) = 13/5
- sec t = 1/cos t = 1/(-12/13) = -13/12
- cot t = 1/tan t = 1/(-5/12) = -12/5