Question

# The rectangular coordinates of a point are given (-5, 2) . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

The rectangular coordinates of a point are given $$(-5, 2)$$ . Use a graphing utility in radian mode to find polar coordinates of each point to three decimal places.

2021-02-12

Rec tan gular coordinates $$= ( x, y) = (-5, 2)$$ Polar coordinates $$= (r, \theta)$$ Then, formula for finding r and theta, is given by - $$r = \sqrt{x^2 + y^2}$$
$$r = \sqrt{(-5)^2 + (2)^2}$$
$$r = \sqrt{(25 + 4)}$$
$$r = \sqrt{29}$$
$$r = 5.385$$ And, $$\theta = \tan^{-1} (\frac{y}{x})$$
$$\theta = \tan^{-1} (\frac{2}{-5})$$
$$\theta = \tan^{-1} (\frac{2}{5}) [\tan^{-1} (-x) = - \tan^{-1} (x)]$$
$$\theta = -0.380$$ radians Polar coordinates $$= (r, \theta) = (5.385, - 0.380)$$