Question

# The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for 0 < 2.

The rectangular coordinates of a point are (4, −4). Plot the point and find two sets of polar coordinates for the point for $$0 < 2$$.

2021-02-05

Given, $$(x, y) = (4, −4)$$ For the polar coordinates $$r = \sqrt{x^2 + y^2}\ and\ \theta = tan^−1 (\frac{y}{x})$$
$$r = \sqrt{16 + 16}$$
$$r = \sqrt{32}$$
$$r = 4 \sqrt 2$$ And $$\theta = tan^-1 (\frac{-4}{4}$$
$$\theta = tan^-1 (-1)$$
$$\theta = \frac{\pi}{4}$$ The two sets of polar coordinates are $$(-4 \sqrt2, \frac{\pi}{4}). (4 \sqrt2, \frac{\pi}{4})$$