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Decomposing vectors

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1. Homework Statement
The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector.

2. Homework Equations

x = |R|cos(theta)

3. The Attempt at a Solution

I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis?
 

Geofleur

Science Advisor
Gold Member
423
176
Both ways are fine, as long as you don't try to memorize a rule and blindly apply it. Personally, I like the first approach, and just tack on the negative sign when I know there should be one.
 

SteamKing

Staff Emeritus
Science Advisor
Homework Helper
12,794
1,665
1. Homework Statement
The magnitude of the vector is 6 m, and points 35 degrees north of west. Find the x component of the vector.

2. Homework Equations

x = |R|cos(theta)

3. The Attempt at a Solution

I am confused about what degrees to input into the cosine function. I know that the vector is pointing 35 degrees north of west, which means that the x component will be negative, but there are two ways I could do it am I am not sure which one I should do. First, I could tack on a negative and calculate -(6 m)cos35 = -4.9 m. Another way is not tack on a negative and calculate (6 m)cos145 = -4.9 m. Which method is better, and which one should I use on a regular basis?
Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up?

East = 0°
North = 90°
West = 180°
South = 270°
 
1,456
44
Well, you could learn the angles for the cardinal points of the compass, but why do that when you can just make something up?

East = 0°
North = 90°
West = 180°
South = 270°
Huh?
 

SteamKing

Staff Emeritus
Science Advisor
Homework Helper
12,794
1,665
You've never seen the following diagram (or a similar one)?:



ucad.gif


It should have been used when you studied trigonometry.

After all,
cos (0°) = 1.0
sin (0°) = 0.0

cos (90°) = 0.0
sin (90°) = 1.0

cos (180°) = -1.0
sin (180°) = 0.0

cos (270°) = 0.0
sin (270°)= -1.0

etc., etc.
 

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