Given that csc = -13/5 for π < t < (3 π)/2, use an appropriate identity to find the value of cot(t). What is cot(t)?

Since cosecant is 1/sin(t), set up a proportionality of -13/5 = 1/sin(t) then you get t = arcsin(-5/13). This means cotangent of t would be 1/tan(arcsin(-5/13)). Which is -2.4 or -12/5. But since π < t < (3 π)/2, cot(t) should be positive. Meaning that it is 12/5 or 2.4… right?