If the terminal side of angle tt goes through point (x,y)(x,y) on the unit circle, then:
\(\displaystyle{\cos{{\left({t}\right)}}}={x}{\quad\text{and}\quad}{\sin{{\left({t}\right)}}}={y}\)

Since \(\displaystyle{x}=-{\left(\frac{{5}}{{13}}\right)}\), then: \(\displaystyle{\cos{{\left({t}\right)}}}=-{\left(\frac{{5}}{{13}}\right)}\)

Since \(\displaystyle{x}=-{\left(\frac{{5}}{{13}}\right)}\), then: \(\displaystyle{\cos{{\left({t}\right)}}}=-{\left(\frac{{5}}{{13}}\right)}\)