Question

Find the rectangular coordinates of the point with the polar coordinates (8, 3 divided by 2 pi).

Answer 1

Answer on Question #45121 – Math – Analytic Geometry

Question. Find the rectangular coordinates of the point with the polar coordinates $(8,\frac{3}{2}\pi)$.

Solution. Recall that the relation between rectangular $(x,y)$ and polar coordinates $(r,\phi)$ is given by the following formulas:

$$x = r \cos \phi, \qquad y = r \sin \phi.$$

In our problem

$$r = 8, \qquad \phi = \frac{3}{2} \pi.$$

Therefore

$$x = r \cos \phi = 8 \cdot \cos \left(\frac{3}{2} \pi\right) = 8 \cdot 0 = 0,$$ $$y = r \sin \phi = 8 \cdot \sin \left(\frac{3}{2} \pi\right) = 8 \cdot (-1) = -8.$$

Thus the rectangular coordinates of the point with the polar coordinates $(8,\frac{3}{2}\pi)$ are

$$(0, -8).$$

Answer. $(0, -8)$.

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