Question

Another representation, in polar coordinates, of the point (157) is -18 6 117 6

Answer 1

Recall that in polar coordinates:

$(r,\theta)=(-r,\theta+\pi)\text{.}$

1) Notice that:

$\frac{11\pi}{6}=\frac{5\pi+6\pi}{6}=\frac{5\pi}{6}+\pi$

2) Using the first equation we get:

$(1,\frac{5\pi}{6})=(-1,\frac{5\pi}{6}+\pi)=(-1,\frac{11\pi}{6})\text{.}$

Answer: -1.