Question

Convert r=tanθ into rectangular form

Answer 1

`√(x^2+y^2) = (y)/(x)`

Explanation:

Convert the expression given equation in polar coordinates to rectangular coordinates.

`r=\tan\theta`

`\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=√(x^2+y^2)\\\\\theta=\tan^(-1)((y)/(x))\end{array}\right}`

`r=\tan\theta\\\\\\\Longrightarrow √(x^2+y^2) = \tan\theta\\\\\\\Longrightarrow √(x^2+y^2) = \tan(\tan^(-1)\Big((y)/(x) \Big))\\\\\\\Longrightarrow \boxed{√(x^2+y^2) = (y)/(x) }`

Thus, the problem is solved.