Answer
$$tan \space t = -2$$ $$sin \space t = \frac{2\sqrt 5}{5}$$ $$cos \space t = -\frac{\sqrt 5}{5}$$ $$sec \space t = -\sqrt 5$$
Work Step by Step
$$cot \space t = \frac{1}{tan\space t} \longrightarrow tan \space t = \frac{1}{cot \space t} = \frac{1}{-1/2} = -2$$ $$csc \space t = \frac{1}{sin\space t} \longrightarrow sin \space t = \frac{1}{csc \space t} = \frac 1 {\sqrt 5/2} = \frac 2 {\sqrt 5} = \frac{2\sqrt 5}{5}$$
$$tan \space t = \frac{sin \space t}{cos \space t} \longrightarrow cos \space t = \frac{sin \space t}{tan \space t}$$ $$cos \space t = \frac{\frac{2\sqrt 5}{5}}{-2} = -\frac {\sqrt 5} 5$$ $$sec \space t = \frac{1}{cos \space t} = \frac{1}{-\frac{\sqrt 5} 5} = -\frac {5}{\sqrt 5} = -\sqrt 5$$
