How do you convert the Cartesian coordinates (10,10) to polar coordinates?

1 Answer
Aug 6, 2015

Cartesian: (10;10)

Polar: (10sqrt2;pi/4)

Explanation:

The problem is represented by the graph below:

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In a 2D space, a point is found with two coordinates:

The cartesian coordinates are vertical and horizontal positions (x;y).

The polar coordinates are distance from origin and inclination with horizontal (R,alpha).

The three vectors vecx, vecy and vecR create a right triangle in which you can apply the pythagorean theorem and the trigonometric properties. Thus, you find:

R=sqrt(x^2+y^2)

alpha=cos^(-1)(x/R)=sin^(-1)(y/R)

In your case, that is:

R=sqrt(10^2+10^2)=sqrt(100+100)=sqrt200=10sqrt2

alpha=sin^(-1)(10/(10sqrt2))=sin^(-1)(1/sqrt2)=45°=pi/4