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

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Homework Help Overview

The discussion revolves around the concept of vector components, specifically addressing whether a vector with an angle greater than 180 degrees can have a negative magnitude. The original poster is working with a vector of 260 km at an angle of 48 degrees south of east and is uncertain about the sign of the vector's magnitude.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to determine the correct sign for the vector components based on the angle provided. Some participants discuss the conventions of angle measurement and the implications for the sine and cosine functions in different quadrants.

Discussion Status

Participants have offered insights into the conventions of angle measurement, noting that counterclockwise is considered positive while clockwise is negative. There is an ongoing exploration of why sine values may be negative in certain quadrants, particularly in relation to the original poster's question about the vector's components.

Contextual Notes

The original poster is grappling with the interpretation of angles and magnitudes in the context of vector components, which may be influenced by specific homework guidelines or conventions not fully detailed in the discussion.

SaltyBriefs
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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??
 
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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.
 
Last edited:
WatermelonPig said:
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? O.o
 
SaltyBriefs said:
Thank you this helped so much! But um just a quick question, why is sin negative? O.o

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

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