Question

How to use unit circle to evaluate the six trig functions of theta

Answer 1

All you need to know is that sin(x) is the y-value of the coordinate point and cos(x) is the x-value of the coordinate point. From here, tan(x) is just sin(x)/cos(x).
That's three of them already. sec(x) is 1/cos(x), csc(x) = 1/sin(x) and cot(x) = 1/tan(x).
Just to recap:

$cos(x) = x-value$
$sin(x) = y-value$
$tan(x) = \frac{sin(x)}{cos(x)}$
$csc(x) = \frac{1}{sin(x)}$
$sec(x) = \frac{1}{cos(x)}$
$cot(x) = \frac{1}{tan(x)} = \frac{cos(x)}{sin(x)}$

And you are done!