polar coordinates

[iluvblueroses]

3, 4pi/3
my book says it converts to 240 degrees but I don't understand how,

 

[tkhunny]

2 pi is 360 degrees
1 pi is 180 degrees

1/3 pi is 60 degrees

4/3 = 1 + (1/3), thus 180 degrees + 60 degrees.

The 3 out front is a distance from the origin and does not contribute to the direction.

 

[galactus]

If you want to convert from radians to degrees, multiply by \(\displaystyle \frac{180}{\pi}\)

This is because, as tkh pointed out, there are 180 degrees in \(\displaystyle \pi\) radians.

Thus, a full circle of 360 degrees is \(\displaystyle 2\pi\) radians.

\(\displaystyle \frac{4\pi}{3}\cdot \frac{180}{\pi}=240\)

If you want to convert from degrees to radians, multiply by \(\displaystyle \frac{\pi}{180}\)