Why is (B.y) for the y-component negative for sin30?

[yardy_genius]

Hello, can someone please explain why (B.y) for the y-component is negative for the sin30. thanks .
question is below.

[PLAIN]http://img710.imageshack.us/img710/6150/resulant.jpg

 

[WJSwanson]

The y-component for the sin30 is because it's actually sin(-30): the angular displacement is in the opposite direction of the reference positive direction. Intuitively, this makes sense because when you add the vectors in component form you would get a vector whose y-component is greater than the y-component of the 8.00N @ 40degrees vector despite the fact that the vectors shown are traveling in opposite directions from the x-axis, that is, their y-components should have opposite signs.

 

[cepheid]

Welcome to PF yardy_genius,

It's just a sign convention. By convention, you're taking "up" to be the positive y-direction and "down" to be the negative y-direction. You could just as easily adopt the opposite sign convention. All that matters is that you pick a convention and stick to it (i.e. use it consistently throughout the problem).

 

[yardy_genius]

The y-component for the sin30 is because it's actually sin(-30): the angular displacement is in the opposite direction of the reference positive direction. Intuitively, this makes sense because when you add the vectors in component form you would get a vector whose y-component is greater than the y-component of the 8.00N @ 40degrees vector despite the fact that the vectors shown are traveling in opposite directions from the x-axis, that is, their y-components should have opposite signs.

thanks a lot

 

[yardy_genius]

Welcome to PF yardy_genius,

It's just a sign convention. By convention, you're taking "up" to be the positive y-direction and "down" to be the negative y-direction. You could just as easily adopt the opposite sign convention. All that matters is that you pick a convention and stick to it (i.e. use it consistently throughout the problem).

thanks , you guys really helped a lot

 

[WJSwanson]

No problem; glad I could help. Cepheid's answer is also pretty important, by the way. He touched on a way more critical point than I did, which is that you can use almost any convention that's convenient, so long as you stick to it (and make sure to revert it to the original terms if necessary/requested).