What is the polar form of ( 5,114 )(5,114)?

1 Answer

(\sqrt{14021}, \tan^{-1}(22.5))(14021,tan1(22.5))

Explanation:

The Cartesian coordinates of the point (x, y)\equiv(5, 114)(x,y)(5,114)

then its polar coordinates (r, \theta)(r,θ) are given as follows

r=\sqrt{x^2+y^2}=\sqrt{5^2+114^2}=\sqrt{13021}r=x2+y2=52+1142=13021

\tan\theta=\frac{y}{x}=\frac{114}{5}tanθ=yx=1145

theta=tan^{-1}(22.8)θ=tan1(22.8)

\therefore (r, \theta)\equiv(\sqrt{13021}, \tan^{-1}(22.5))