Question

find the polar coordinates whose cartesian coordinates are (0,1/2)​

Answer 1

SOLUTION

TO DETERMINE

The polar coordinates whose cartesian coordinates are

$\displaystyle \sf{ \bigg(0 \: , \frac{1}{2} \bigg)}$

EVALUATION

Let (r, θ) be the polar coordinates of the point

Then

$\displaystyle \sf{ 0 = r \cos \theta \: \: , \frac{1}{2} =r \sin \theta}$

Now Squaring and adding we get

$\displaystyle \sf{ {r}^{2} = \frac{1}{4} }$

$\displaystyle \sf{ \implies \: r = \frac{1}{2} }$

Again

$\displaystyle \sf{ tan \theta = \frac{ \displaystyle \sf{ \frac{1}{2}} }{0} }$

$\displaystyle \sf{ \implies \: tan \theta = \infty }$

$\displaystyle \sf{ \implies \: tan \theta = \infty }$

$\displaystyle \sf{ \implies \theta = \frac{\pi}{2} }$

Hence the required polar coordinates

$\displaystyle \sf{ \bigg( \frac{1}{2} \: , \frac{\pi}{2} \bigg)}$

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