Question

appoint and rectangular coordinates is given convert the point to polar coordinates around your answer to two decimal places. (5,7)

Answer 1

We can convert rectangular coordinates of the form (x, y) to polar coordinates (r, θ) by means of the following formulas:

$\begin{gathered} r=\sqrt[]{x^2+y^2} \\ \end{gathered}$$\theta=\tan ^{-1}(\frac{y}{x})$

In this case, we are given the point (5, 7), by replacing 5 for x and 7 for y, we get:

$r=\sqrt[]{5^2+7^2}=\sqrt[]{25+49}=\sqrt[]{74}$$\theta=\tan ^{-1}(\frac{7}{5})=54.46$

in polar coordinates, we usually give the value of θ in radians, we've calculated θ in degrees, then we have to convert it, like this:

$\theta=54.46\times\frac{\pi}{180}=0.95$

Then, the given point in polar coordinates is (√74, 0.95)