**Problem : **
Why do the following pairs of functions always have the same sign: sine
and cosecant, cosine and secant, tangent and cotangent?

These function pairs are reciprocals.

**Problem : **
In which quadrant do the most trigonometric
functions have negative signs?

In quadrants II, III, and IV, four out of the six trigonometric functions have
negative signs. In quadrant I none of the trigonometric functions have negative
signs. Quadrants II, III, and IV are tied for having the most trigonometric
function with negative signs.

**Problem : **
Which value in the following group is not equal to the others:
sin(),
cos(*Π*), cot(), sec(0)?

sec(0) = 1. The rest are equal to -1.

**Problem : **
When *θ* = *Π*, which two trigonometric functions are undefined?

Cosecant and cotangent