Question

Find the polar co-ordinates of points whose Cortesion co-ordinates is (5, 5).

Answer 1

Answer:

$r \cos( \alpha ) = 5 \\ \\ r \sin( \alpha ) = 5 \\ \\ \\ {r}^{2} ( { \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} ) = {5}^{2} \\ \\ {r}^{2} = 25 \\ \\ r = 5 \: units \\ \\ \frac{r \sin( \alpha ) }{r \cos( \alpha ) } = \frac{5}{5 } \\ \\ \tan( \alpha ) = 1 \\ \\ \alpha = 45 \: degrees = \frac{\pi}{4} \\ \\ therefore \: polar \: coordinates \: are \: \: \: (r \: \: \: \: \: \alpha ) = (5 \: \: \: \: \: \: \: \frac{\pi}{4} )$