I Did I Make a Mistake in my Coordinates? Help Needed!

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The discussion revolves around the correct coordinates of point B, initially questioned as either (a cos theta, a sin theta) or (-a cos theta, a sin theta). Participants clarify that the labeling in the diagram is accurate, noting that cos theta is negative in the second and third quadrants. The confusion arises from treating the x-coordinate as a positive length without considering its position relative to the origin. Ultimately, the correct interpretation confirms that the x-coordinate should indeed be negative based on the defined origin. The clarification resolves the initial misunderstanding.
Shafia Zahin
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In the attached pic,it is shown that the coordinates of point B are (a cos theta, a sin theta) ,but shouldn't it be (-a cos theta,a sin theta)? Can anybody please help?
 

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No there is nothing wrong with the labeling of the coordinates in the diagram. Recall that ##\cos \theta## is negative for ##\pi/2 < \theta < 3\pi/2## (or what you may know as the second and third quadrants).
 
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Fightfish said:
No there is nothing wrong with the labeling of the coordinates in the diagram. Recall that ##\cos \theta## is negative for ##\pi/2 < \theta < 3\pi/2## (or what you may know as the second and third quadrants).
But didn't it come like this?(see the attachment)
 

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When you did the triangle construction in your diagram, you treated ##x## there as a length, which only takes on positive values, but ignored its position relative to where the origin was defined. So, the x-coordinate of the point should in fact be the negative of the ##x## in your derivation.
 
Fightfish said:
When you did the triangle construction in your diagram, you treated ##x## there as a length, which only takes on positive values, but ignored its position relative to where the origin was defined. So, the x-coordinate of the point should in fact be the negative of the ##x## in your derivation.
Oh,now I got it,thank you so much:smile:
 
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