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

1.	Find the polar coordinate of the point (1,2)
Answer» 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)

Answer»

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)

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