Question

the polar coordinates of the point whose cartesian coordinates are 1/√2 , -1/√2​

Answer 1

Given,

Cartesian coordinates are given (1/√2, -1/√2​)

To find,

The polar coordinates of given catesian coordinates(1/√2, -1/√2​).

Solution,

We can simply find the polar coordinates by given cartesian coordinates.

Let the required polar coordinates by (r, Ф)

 x = 1/√2, y=-1/√2

r = √(x²+y²)

r= √(1/2+1/2)

r= √(1)

r= 1

Now, tan Ф = y/x

        tanФ= -1

             Ф = (л-л/4)

             Ф = 3л/4

             Ф = 3л/2+3л/4

              Ф = 9л/4

                (1, 9л/4)

Hence, the polar coordinates of the point whose cartesian coordinates are (1/√2, -1/√2​) are (1, 9л/4).