TBR Physics Section 2 Passage IX (Tension)

[golgiapparatus88]

So the question is pretty much, "which way (or ways) would be easiest to move a large block. Theta = 0, Theta = 30, or Theta is 30 below the x-axis (330 degrees).

I understand why 30 degrees above the x-axis would decrease tension but technically, shouldn't 30 degrees below the x-axis work also? Cos330 is .866 just like cos30 is .866. And from what I remember in trig, the 4th quadrant has a positive cosine too. I know that pulling a block into the ground wouldn't be beneficial in real life but mathematically speaking, shouldn't it? Or else I'm looking at it wrong.

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[BerkReviewTeach]

So the question is pretty much, "which way (or ways) would be easiest to move a large block. Theta = 0, Theta = 30, or Theta is 30 below the x-axis (330 degrees).

I understand why 30 degrees above the x-axis would decrease tension but technically, shouldn't 30 degrees below the x-axis work also? Cos330 is .866 just like cos30 is .866. And from what I remember in trig, the 4th quadrant has a positive cosine too. I know that pulling a block into the ground wouldn't be beneficial in real life but mathematically speaking, shouldn't it? Or else I'm looking at it wrong.

Your angle perspective is good at first glance, but you also have to consider how kinetic friction will be impacted. If you pull down on the rope, part of the force is pushing down on the box. The normal force increases as a result, having to now offset the weight of the box and a component of the tension. A greater normal force results in greater kinetic friction, which makes it harder to pull. It'd be like setting a weight on top of the box.