# X an y components of a vector

## Homework Statement

what are the x and y components of a vector a in the xy plane if its direction is 210(degrees) counterclockwise from the positive direction of the x axis and its magnitude is 14 m.

## Homework Equations

vector is in the third quadrant with an angle of 30(degrees)

## The Attempt at a Solution

i got the angle to be 30(degrees) so i just did

14sin30 for the x component = 7.0
14cos30 for the y component = 12.1

should they both be negative since there in the third quadrant or do the negatives cancel to get a positive.

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Char. Limit
Gold Member
Negatives cancel only when you multiply them. Since you aren't multiplying here, both parts are negative.

would my answers be correct then

x = -7.0

y= -12.1

Char. Limit
Gold Member
That seems right, yes.

Although, if significant figures were important, the y component might have to be rounded... I'm not sure how important they are here.

14.cos 30=x . if it is 30 degree to x (210), x have to be bigger than y. (to correct)

well if its 210(degrees) counterclockwise then wouldnt the angle be 30(degrees) sin 210-180 = 30 degrees

14.cos 30=x . if it is 30 degree to x (210), x have to be bigger than y. (to correct)
why would x be cos and not y. if the vector is in the third quadrant and cos is adjacent/hypotenuse then adjacent would be x so the only side left would be y which you would be solving for.

Char. Limit
Gold Member
why would x be cos and not y. if the vector is in the third quadrant and cos is adjacent/hypotenuse then adjacent would be x so the only side left would be y which you would be solving for.
I'm not sure what you mean...

If you mean that the x component should correspond to the cosine, this is because the cosine of the angle measures the length of the adjacent side to the angle, in this case, the x-axis.

ok i got it thanks.

14cos30 = -12.1 x-component
14sin30 = -7.0 y-component