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.

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.

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 $$= (r, \theta) = (5.385, - 0.380)$$

Relevant Questions

The rectangular coordinates of a point are given (2, -2). Find polar coordinates of the point. Express theta in radians.
Polar coordinates of a point are given $$(4, 90^\circ)$$. Find the rectangular coordinates of each point.
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). Find polar coordinates of the point.
Convert the point $$(-\sqrt3, -\sqrt 3)$$ in rectangular coordinates to polar coordinates that satisfies
$$r > 0, -\pi < \theta \leq \pi$$
Convert from polar to rectangular coordinates: $$(2,(\pi/2))\Rightarrow (x,y)$$
Find, correct to four decimal places, the length of the curve of intersection of the cylinder $$\displaystyle{4}{x}^{{2}}+{y}^{{2}}={4}$$ and the plane x + y + z = 5.
Find the solution of limit $$\displaystyle\lim_{{{\left({x},{y}\right)}\rightarrow{0},{0}}}\frac{{\sqrt{{{x}^{2}+{y}^{2}}}}}{{{x}^{2}+{y}^{2}}}$$ by using the polar coordinates system.
Given $$r′(t)=⟨\sec2t,−\sint⟩$$, find the arc length of the curve r(t) on the interval $$[−π/3].$$