How do you find coterminal angles between 0 and 2pi for angles given in pi radians?
add n times 2 pi
or
subtract n times 2 pi
where n can be any counting number
2 pi is a full circle, so every time you go around you end up at the same place.
To find coterminal angles between 0 and 2π for angles given in π radians, you need to add or subtract multiples of 2π. Here's how you can do it:
1. Start with the given angle in π radians.
2. To obtain a coterminal angle, add or subtract multiples of 2π.
3. Add or subtract 2π until you get an angle between 0 and 2π.
For example, let's say you have an angle given as π/3 radians:
1. Start with π/3.
2. Add 2π: π/3 + 2π = (3π + π)/3 = 4π/3. This is one coterminal angle.
3. Add 2π again: 4π/3 + 2π = (12π + 4π)/3 = 16π/3. This is another coterminal angle.
4. Since 16π/3 is greater than 2π, we need to subtract 2π.
Subtract 2π: 16π/3 - 2π = (16π - 6π)/3 = 10π/3. This is another coterminal angle.
5. Continue this process until you find all the coterminal angles between 0 and 2π.
In summary, to find coterminal angles between 0 and 2π for angles given in π radians, add or subtract multiples of 2π until you get an angle within the desired range.