Question

Express the Cartesian coordinates (-2,2) in polar coordinates in at least two different ways. Write the point in polar coordinates with an angle in the range 0

Answer 1

Explanation:

The cartesian coordinates is (-2, 2)

So, x = -2 and y = 2

So, r Cos θ = x and r Sin θ = y

r Cos θ = - 2 .... (1)

r Sin θ = 2 .... (2)

Squarring equation (1) and (2) and add

`r^(2){Sin^(2)\theta +Cos^(2)\theta }= (-2)^(2)+2^(2)`

`r^(2)=8`

r = 2.83

Divide equation (2) by equation (1), we get

`tan\theta  = - 1`

θ = 3π/4

So, the polar coordinates are (2.83 Cos 3π/4, 2.83 Sin 3π/4)