+0

# what polar coordinates represent the same as that of point P(4,30)

0
287
1

what polar coordinates represent the same as that of point P(4,30)

Guest May 13, 2014

#1
+26387
+5

The polar representation of cartesian point (x,y) is (r,θ) where

$$\\ r=\sqrt{x^2+y^2}\\ \theta=\tan^{-1}(\frac{y}{x})$$

So, with x = 4 and y = 30

$${\mathtt{r}} = {\sqrt{{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{30}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{30.265\: \!491\: \!900\: \!843\: \!111\: \!9}}$$

$${\mathtt{theta}} = \underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{30}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{82.405\: \!356\: \!631\: \!409^{\circ}}}$$

Alan  May 13, 2014
Sort:

#1
+26387
+5

The polar representation of cartesian point (x,y) is (r,θ) where

$$\\ r=\sqrt{x^2+y^2}\\ \theta=\tan^{-1}(\frac{y}{x})$$

So, with x = 4 and y = 30

$${\mathtt{r}} = {\sqrt{{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{30}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{30.265\: \!491\: \!900\: \!843\: \!111\: \!9}}$$

$${\mathtt{theta}} = \underset{\,\,\,\,^{{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{30}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{theta}} = {\mathtt{82.405\: \!356\: \!631\: \!409^{\circ}}}$$

Alan  May 13, 2014

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details