Answer
$I$ - All of the functions are positive
$II$ - $sin, csc$
$III$ - $tan, cot$
$IV$ - $cos, sec$
Work Step by Step
Sign of each of the trigonometric functions are defined based on the quadrant of the angle.
In the first quadrant all of the possible values (both $x$-axis and $y$-axis) are positive, so all of the trigonometric functions are positive.
In the second quadrant we have negative $x$ values and positive $y$ values, so only sine and cosecant are positive.
In the third quadrant we have both $x$ and $y$ values negative, so only tangent and cotangent take positive values.
And in the fourth quadrant $x$ values are positive and $y$ values are negative, so only cosine and secant take positive values.
