The angle that a vector makes when it is parallel to x-axis.

[Alshia]

If there is a (displacement) vector parallel to the x-axis, and this vector is below the x-axis, is the angle (in radians) made by this vector ∏ or -∏? Why?

If the vector is above the x-axis, what is the angle? Why?

 

[Infinitum]

If there is a (displacement) vector parallel to the x-axis, and this vector is below the x-axis, is the angle (in radians) made by this vector ∏ or -∏? Why?

If the vector is above the x-axis, what is the angle? Why?

The angle does not depend on which side of the x-axis it lies on. It depends on what the direction of the vector is. Say if it were pointing towards positive x axis, then the angle would be 0. If pointing towards negative x-axis then angle would be ∏.

PS : ∏ and -∏ are the same thing

 

[Mark44]

PS : ∏ and -∏ are the same thing

The reference points on the unit circle for the two angles are the same, but the angles are different. An angle of $\pi$ implies counterclockwise rotation; an angle of -$\pi$ implies clockwise rotation.

 

[Alshia]

Ah, I missed that accidentally. Thanks for the responses.

 

[Infinitum]

The reference points on the unit circle for the two angles are the same, but the angles are different. An angle of $\pi$ implies counterclockwise rotation; an angle of -$\pi$ implies clockwise rotation.

Oh, yes. I was only speaking of them in the sense that they would put you in the same direction after rotation.