Question

Find the polar coordinate of the point (1,2)

Answer 1

Let Polar coordinate if point (1,2) is (r,θ)

We know the relation of cartesian coordinates (x, y) with polar coordinates (r,θ) is

x = rcosθ  \(\Rightarrow\) rcosθ = 1 .............(1)

y = rsinθ \(\Rightarrow\) rsinθ = 2 .............(2)

dividing equation (2) by equation (1), we get

tanθ = 2 \(\Rightarrow\) θ = tan^-12 = 1.107

Now, adding square of equation (1) and square of equation (2)

we get,

r²cos²θ + r²sin²θ = 1+4

r² = 5 \(\Rightarrow\) r = \(\sqrt5\)

therefore, polar coordinates of (1,2) is (\(\sqrt5\),1.107) or (\(\sqrt5\),tan^-12)