Let $P(t)=(x, y)$ be the terminal point on the unit circle that corresponds to the real number $t$. Find the values of sec $t$, csc $t$, and cot $t$. \[ P=\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right) \] \[ \sec \mathrm{t}= \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \operatorname{csct}= \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) \[ \cot \mathrm{t}= \] (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Step 1 ：Let's denote the point \(P(t)=(x, y)\) as \(\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)\).

Step 2 ：Since \(P(t)\) is a point on the unit circle, we can use the definitions of secant, cosecant, and cotangent in terms of the coordinates of the point on the unit circle.

Step 3 ：The secant of \(t\) is defined as the reciprocal of the x-coordinate, so \(\sec t = -\frac{2}{\sqrt{3}} = -\frac{2\sqrt{3}}{3}\).

Step 4 ：The cosecant of \(t\) is defined as the reciprocal of the y-coordinate, so \(\csc t = -\frac{2}{1} = -2\).

Step 5 ：The cotangent of \(t\) is defined as the x-coordinate divided by the y-coordinate, so \(\cot t = \frac{\sqrt{3}}{2} / \frac{1}{2} = \sqrt{3}\).

Step 6 ：So, the values of \(\sec t\), \(\csc t\), and \(\cot t\) are \(-\frac{2\sqrt{3}}{3}\), \(-2\), and \(\sqrt{3}\) respectively.