91Ó°ÊÓ

First, identify in which quadrant the angle falls. The given value \( t=2\pi / 3 \) is greater than \( \pi / 2 \) and less than \( \pi \), so it lies in the second quadrant.

In the second quadrant, only sine and its reciprocal function cosecant are positive. You can use the following equations for exact values:\n1. Sin: Based on the relation \( \sin(\pi - \theta) = \sin(\theta) \), we can write \( \sin(2\pi / 3)= \sin(\pi - 2\pi / 3) = \sin(\pi / 3) = \sqrt{3}/2 \). \n2. Cos: As cosine is negative in the second quadrant, \( \cos(2\pi / 3)= -\cos(\pi - 2\pi / 3) = -\cos(\pi / 3) = -1/2 \). \n3. Tan: Considering that tan function is negative in the second quadrant, and \( \tan(\theta) = \sin(\theta)/\cos(\theta) \), hence \( \tan(2\pi / 3) = \sin(2\pi / 3) / \cos(2\pi / 3) = \sqrt{3}/2 / -1/2 = -\sqrt{3} \). \n4. Cosec, sec, cot: These are reciprocal of sin, cos, tan respectively. You can calculate these values by taking reciprocal of sin, cos, and tan.

Therefore, the values of the trigonometric functions at \( t=2\pi / 3 \) are: \( \sin(2\pi / 3) = \sqrt{3}/2 \), \( \cos(2\pi / 3) = -1/2 \), \( \tan(2\pi / 3) = -\sqrt{3} \), \( \csc(2\pi / 3) = 2/\sqrt{3} \), \( \sec(2\pi / 3) = -2 \), \( \cot(2\pi / 3) = -1/\sqrt{3} \).