SOLUTION: find an angle between 0 and 2pi that is coterminal with: (27pi)/10, coterminal with (-pi)/6, coterminal with (-19pi)/10, and lastly coterminal with (13pi)/3

I'll only do the first two, the other two are done the same way:


To find coterminal angles we add  to the angle, where
n is some integer, positive, negative, or zero.   

Therefore when we find n, the answer will be 

Since we want the coterminal angle to be between 0 and , 
we write an inequality which indicates that:



Divide through by 



Multiply through by 10



Subtract 27 from all three sides:



Divide through by 20





There is only one integer between -1.35 and -0.35, namely -1.

So n = -1, therefore the answer is








----------------------

 

Same way:

We add  and the answer will be , when we find n.

Since we want the coterminal angle to be between 0 and , 
we write the inequality which indicates that:



Divide through by 



Multiply through by 6



Add 1 to all three sides:



Divide through by 12


      


There is only one integer between  and , namely 1.

So n = 1, therefore the answer is







---------------------

Edwin