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Section 9.6 : Polar Coordinates

2. The polar coordinates of a point are $$\left( { - 5,0.23} \right)$$. Determine the Cartesian coordinates for the point.

Show Solution

There really isnâ€™t too much to this problem. From the point we can see that we have $$r = - 5$$ and $$\theta = 0.23$$(in radians of course!). Once we have these all we need to is plug into the formulas from this section to get,

$x = r\cos \theta = \left( { - 5} \right)\cos \left( {0.23} \right) = - 4.8683\hspace{0.25in}y = r\sin \theta = \left( { - 5} \right)sin\left( {0.23} \right) = - 1.1399$

So, the Cartesian coordinates for the point are then,

$\require{bbox} \bbox[2pt,border:1px solid black]{{\left( { - 4.8683,\, - 1.1399} \right)}}$