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

[Shafia Zahin]

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?

 

[Fightfish]

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).

 

[Shafia Zahin]

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)

 

[Fightfish]

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.

 

[Shafia Zahin]

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