Finding the Components of a Vector in the Third Quadrant

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To find the components of a vector in the third quadrant with a direction of 210 degrees and a magnitude of 14 m, the x and y components are calculated using trigonometric functions. The correct calculations yield x = -12.1 m and y = -7.0 m, as both components are negative due to their position in the third quadrant. The confusion regarding the use of sine and cosine is clarified by noting that cosine corresponds to the x-component (adjacent side) and sine to the y-component (opposite side). Significant figures may need to be considered, particularly for the y-component. The final components are confirmed as x = -12.1 and y = -7.0.
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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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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
 
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 wouldn't the angle be 30(degrees) sin 210-180 = 30 degrees
 
mechmech said:
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.
 
anybody please
 
jpd5184 said:
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.
 
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ok i got it thanks.

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