Question

The rectangular coordinates of a point are (-4, 4). Find polar coordinates of the point.

The rectangular coordinates of a point are (-4, 4). Find polar coordinates of the point.

2021-02-10

We have been given the rectangular coordinates (-4,4) and we have to find the polar coordinates of the points. as we know that $$r = \sqrt(x^2 + y^2)$$ now as rectangular coordinates are (x, y) and polar coordinates are $$(r, \theta)$$. $$r = \sqrt{(-4)^2 + 4^2}$$
$$r = \sqrt{16 + 16}$$
$$r = \sqrt{32}$$
$$r = 4\sqrt 2$$ now as we know that $$\alpha = tan^−1 \frac{y}{x}$$ $$a = tan^-1 \frac{4}{-4}$$
$$a = tan^-1 (-1)$$
$$a = - \frac{\pi}{4}$$
$$\theta = -\pi/4 + \pi = \frac{3\pi}{4}$$
$$\theta = \frac{3\pi}{4}$$ now The required polar coordinate $$=(4\sqrt 2, 3\frac{\pi}{4})$$