Question

Express the cartesian coordinates (1,-1) in polar coordinates in at least two different ways.

Answer 1

`(√(2), (7\pi )/(4))` or

`(√(2),5.5)` (using the angle in the radian form)

Explanation:

Here, we want to write the given rectangular coordinate in its polar form

Mathematically, we start by identifying the quadrant in which we have the point

The point is located in the the fourth quadrant

We have the general polar coordinate form as;

(r,θ)

where;

`r = \sqrt({x}^(2) +y^(2) )\\\\r = \sqrt({-1}^2+1^2) = \sqrt2`

We have the theta value calculated as;

theta = arc tan (y/x)

y = -1 and x = 1

theta = arc tan (-1/1)

theta = arc tan (-1)

theta = 45+270 = 315

So, we have the polar coordinate expression as;

`(√(2), (7\pi )/(4))`

or in radians as;

`(√(2), 5.5)`