Determine the exact value of the given function.

sin (π/6)

Determine the exact value of the given function.

tan (π/3)

Determine the exact value of the given function.

sec (π/4)

Determine the exact value of the given function.

tan (2π/3)

The circle with a radius of one unit is partitioned into twelve equal arcs, where each arc corresponds to specific $t$-values. Determine the value of each trigonometric function at the given real number $t$ using the $(x,y)$ coordinates in the diagram or specify that the expression is undefined.

$\sin \frac{\pi }{6}$

Using the unit circle, determine the value of $\tan\frac{4\pi}{3}$.

The circle with a radius of one unit is partitioned into eight equal arcs, where each arc corresponds to specific $t$-values. Determine the value of each trigonometric function at the given real number $t$ using the $\left(x,y\right)$ coordinates in the diagram or specify that the expression is undefined.

$\sin\frac{7\pi}{4}$