Question

If the rectangular coordinates of a point are given by (6, y), and its polar coordinates are (r, 22°), determine the value of y and r.

Answer 1

Rectangular coordinates: (6, y), polar coordinates (r, $22{}^{\circ}$).

We know that $x = r \cos(\alpha y) = 6.47 \cdot \sin(22{}^{\circ})$, $r = 6 / \cos(22{}^{\circ}) = 6.47$.

For $y$ we have:

$$y = r \cdot \sin(\alpha y) = 6.47 \cdot \sin(22{}^{\circ}) = 2.42$$

So we get

rectangular coordinates: (6, 2.42),

polar coordinates: $(6.47, 22{}^{\circ})$.