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 : Which value in the following group has a different sign from the others: sin(), sec(), cot(), cos()?

sec() is the only negative value in the group.

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

Cosecant and cotangent
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