What is the distance between (4 ,( 9 pi)/8 )(4,9π8) and (-4 ,( 3pi )/2 )(4,3π2)?

1 Answer

6.6517\ \text{unit}

Explanation:

The distance between the points (r_1, \theta_1)\equiv(4, {9\pi}/8) & (r_2, \theta_2)\equiv(-4, {3\pi}/2) is given by the formula as follows

\sqrt{r_1^2+r_2^2-2r_1r_2\cos(\theta_1-\theta_2)}

=\sqrt{4^2+(-4)^2-2(4)(-4)\cos({9\pi}/8-{3\pi}/2)}

=\sqrt{32+32\cos({3\pi}/8)}

=4\sqrt2\sqrt{1+\sin({\pi}/8)}

=6.6517\ \text{unit}