Can Vectors with an angle 180(degrees+) have a negative magnitude?

[SaltyBriefs]

Homework Statement

Can vectors with 180+(degrees) have a negative magnitude? I'm trying to find components of a vector that is going 260 km, 48 (degrees) south of east. So I'm confused whether the 260 is positive or not because of the -48 degrees.

Homework Equations

($\vec{V}$) (sin$\theta$)
($\vec{V}$) (cos$\theta$)

The Attempt at a Solution

(-260km)(sin(48)) or (260km)(sin(48)) =$\vec{V}$$_{y}$

(-260km)(cos(48)) or (260km)(cos(48)) =$\vec{V}$$_{x}$

Which one??

 

[WatermelonPig]

sin(x) = -sin(-x)

cos(x) = cos(-x)

Hope that helps.

Just use the convention that counterclockwise is postive and clockwise is negative in terms of measuring an angle.

 

[SaltyBriefs]

sin(x) = -sin(-x)

cos(x) = cos(-x)

Hope that helps.

Just use the convention that counterclockwise is postive and clockwise is negative in terms of measuring an angle.

Thank you this helped so much! But um just a quick question, why is sin negative?

 

[SaltyBriefs]

Thank you this helped so much! But um just a quick question, why is sin negative?

Oh wait is this from cos, sin
and since it is in the 4th quadrant, y is negative (sin) and x is positive (cos)

 

[rwisz]

I would like to clarify that vectors with an angle of 180 degrees or greater can have a negative magnitude. This is because the magnitude of a vector is simply the length of the vector, which can be positive or negative depending on the direction of the vector. The angle of a vector only represents the direction, not the magnitude.

In the given problem, the 260 km is the magnitude of the vector, and the -48 degrees represents the direction. So, the magnitude is positive while the direction is negative. This means that the vector is going in a south of east direction, but the magnitude is still positive. Therefore, you should use the positive value of 260 km in your calculations for the components of the vector.

In general, when dealing with vectors, it is important to pay attention to both the magnitude and direction separately, as they are two distinct properties of a vector. I hope this helps clarify any confusion!