Problem 17E

Converting coordinates Express the following polar coordinates in Cartesian coordinates.

Solution 17E

Step 1:

In this problem we have to express the given polar coordinates ( 1, ) in cartesian coordinates.

To convert polar coordinates ( r , to Cartesian coordinate (x , y) is ;

X = r cos(

Y = r sin(

Given polar coordinates ( r , = ( 1, )

So , x = r cos(= (1) cos()

= cos() , since cos( -x) = cos(x)

= , since cos() = .

y = r sin( = (1) sin()

= -sin() , since sin(-x) = -sin(x)

= , since sin() = .

Hence the cartesian co-ordinates are ( x, y) = ( , )