Answer:
In degrees : [tex]\bf -600^o,-240^o,120^o,480^o[/tex]
In radians : [tex]\displaystyle\bf-\frac{10}{3}\pi,-\frac{4}{3} \pi,\frac{2}{3} \pi,\frac{8}{3} \pi[/tex]
Step-by-step explanation:
To find the co-terminal angles for -600°, we can use the co-terminal angles formula:
[tex]\boxed{in\ degrees=\theta\pm360^on}[/tex]
[tex]\boxed{in\ radians=\theta\pm2\pi n}[/tex]
Where:
- [tex]\theta[/tex] = given angle
- [tex]n[/tex] = integer numbers
In degrees:
As the difference between -600° and -720° (the bottom border) is less than 360°, then -600° is the smallest angle for the set. Hence, we start with n = 1:
[tex]-600^o=-600^o+360^o(1)[/tex]
[tex]=-240^o[/tex]
[tex]-600^o=-600^o+360^o(2)[/tex]
[tex]=120^o[/tex]
[tex]-600^o=-600^o+360^o(3)[/tex]
[tex]=480^o[/tex]
Since the difference between 480° and 720° (the top border) is less than 360°, then 480° is the biggest angle for the set. Therefore:
[tex]-600^o\ is\ co-terminal\ with\ \bf-600^o,-240^o,120^o,480^o[/tex]
In radians:
To convert a degree into radian, we use this formula:
[tex]\boxed{radian=\frac{degree}{180^o} \times\pi}[/tex]
[tex]\displaystyle radian\ for\ -600^o=\frac{-600^o}{180^o}\times\pi[/tex]
[tex]\displaystyle=-\frac{10}{3} \pi[/tex]
[tex]\displaystyle radian\ for\ -240^o=\frac{-240^o}{180^o}\times\pi[/tex]
[tex]\displaystyle=-\frac{4}{3} \pi[/tex]
[tex]\displaystyle radian\ for\ 120^o=\frac{120^o}{180^o}\times\pi[/tex]
[tex]\displaystyle=\frac{2}{3} \pi[/tex]
[tex]\displaystyle radian\ for\ 480^o=\frac{480^o}{180^o}\times\pi[/tex]
[tex]\displaystyle=\frac{8}{3} \pi[/tex]
[tex]\displaystyle -600^o\ is\ co-terminal\ with\ \bf-\frac{10}{3}\pi,-\frac{4}{3} \pi,\frac{2}{3} \pi,\frac{8}{3} \pi[/tex]
Notes: You can also convert -720° and 720° into radians, then use the co-terminal angles formula to find the solutions.
