How do you convert $(5sqrt 3, −5)$ to polar form?

Question

5296 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-21T05:43:25

Polar form of $(5sqrt3,-5)$ are $(10,-pi/6)$

If Cartesian coordinates are $(x,y)$ and its polar coordinates are $(r,theta)$ , then

$r^2=x^2+y^2$ and $tantheta=y/x$

Hence, in case of $(5sqrt3,-5)$

$r=sqrt((5sqrt3)^2+(-5)^2))=sqrt(25xx3+25$

)= $sqrt(75+225)=sqrt100=10$

and as $tanteta=-5/(5sqrt3)=-1/sqrt3$

$theta=-pi/6$

Hence polar form of $(5sqrt3,-5)$ are $(10,-pi/6)$

How do you convert (5sqrt 3, −5)(5sqrt 3, −5) to polar form?