Coterminal angles: are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. In radians, given an angle theta, its coterminal angles are given by:
[tex]\theta\pm2\pi[/tex]
In our problem, we want to find a coterminal angle to 19π/6 on the interval between 0 and 2π. If we subtract 2π from this angle, we're going to find the coterminal angle on this interval:
[tex]\frac{19\pi}{6}-2\pi=\frac{19\pi}{6}-\frac{12\pi}{6}=\frac{(19-12)\pi}{6}=\frac{7\pi}{6}[/tex]
The coterminal angle is 7π/6.
In degrees, given an angle theta, its coterminal angles are given by:
[tex]\theta\pm360^o[/tex]
We want to find an angle between 0° and 360° that is coterminal with -300°, therefore, we must add 360º to our angle:
[tex]-300^o+360^o=60^o[/tex]
The coterminal angle to -300º between 0º and 360º is 60º.
