Cartesian and polar co-ordinates

A diagram representing the point (3, 4) is shown in Fig. 24.2.

From Pythagoras’ theorem, r =√32 + 42 = 5 (note that −5 has no meaning in this context). By trigonometric ratios, θ = tan−1 43 = 53.13◦ or 0.927 rad [note that 53.13◦ = 53.13 × (π/180) rad = 0.927 rad.] Hence (3, 4) in Cartesian co-ordinates corresponds to (5, 53.13◦) or (5, 0.927 rad) in polar co-ordinates.