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

1 Answer
Jan 29, 2016

Answer:

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.