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 positive 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 positive 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)