How do you find the rectangular coordinate of (sqrt 1, 225^o)?

1 Answer
David G.
Jan 29, 2016

I will assume the original coordinates are polar. If (r, theta)=(sqrt1, 225^o) then (x, y)= (-0.7, -0.7).

Explanation:

We use trigonometry to convert polar coordinates to rectangular. See this answer for a more detailed discussion:

http://socratic.org/questions/how-do-you-convert-the-polar-coordinate-4-5541-1-2352-into-cartesian-coordinates

In this case, the hypotenuse is the distance of the point from the origin, in this case sqrt1 units, but the square root of 1 is just 1. The angle from the positive x axis is 225^o.

x= r cos theta = 1*cos 225 = -0.707

y= r sin theta = 1*sin 225 = -0.707

That means the rectangular (sometimes called Cartesian) coordinates of the point in question are (-0.707, -0.707), but we really shouldn't give answers more precise than the data we were given, so round the answer to (-0.7, -0.7).

This makes sense, because 225^o places the point in the 'third quadrant', where both its x and y values are negative numbers.

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