Find an angle between 0 and 2π that is coterminal with −7π.

Question

(1) Find an angle between 0 and 2π that is coterminal with −7π.

(2) Find an angle between 0° and 360° that is coterminal with 1170°

(1) _ radians

(2) _ °

Answer 1

Every time rotate around 2pi in either direction you are back at your starting position so at -7pi ( 3times -2pi plus 1 more -pi) you are at -pi so your co terminal angle is +pi or +180degrees

For 1170 you will use cycles of 360 degrees( one complete rotation ) to see

where you land up 3 x 360 is 1080 so you have gone 90 degrees past there(1170-1080) so your co terminal angle is pi or 90 degrees