Math, asked by anoop80, 1 year ago

Find the polar coordinates of point whose rectangular coordinate are (√3,1)

Answers

Answered by ColinJacobus
6

Answer: The answer is (2,30°).


Step-by-step explanation: Given that the rectangular co-ordinates of a point are (√3,1). We are to find the polar co-ordinates of the given point.

WE know that the relation between rectangular co-ordinates (x,y) and polar co-ordinates (r,β) of a point is given by

x^2+y^2=r^2,~~~\beta=\tan^{-1}\dfrac{y}{x},

where 'r' is called the modulus and 'β' is called the argument. Please see the attached figure for clear understanding of the relationship.

Here,

x=\sqrt 3~~\textup{and}~~y=1.

So,

(\sqrt{3})^2+1^2=r^2\\\\\Rightarrow r^2=3+1\\\\\Rightarrow r^2=4\\\\\Rightarrow r=2,~~\textup{since 'r' is the modulus, so we cannot take to be negative}.

And,

\beta=\tan^{-1}\dfrac{1}{\sqrt 3}=\tan^{-1}\tan 30^\circ=30^\circ.

Thus, the polar co-ordinates of the point are (2,30°).


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