Find a positive and negative angle

Question

Find a positive and negative angle that are co terminal with 9(pi)/5

Answer 1

Since the unit circle is 2π radians, you can find co-terminal angles by adding and subtracting 2π. So...

 

(9π)/5 + 2π = (9π)/5 + (10π)/5 = (19π)/5

 

(9π)/5 - 2π = (9π)/5 - (10π)/5 = -π/5

 

 

There are an infinite number of possible co-terminal angles. (29π)/5, (39π)/5, (49π)/5, ... and (-11π)/5, (-21π)/5, (-31π)/5, ... all work.

Answer 2

9(pi)/5=9(180)/5=9(36)=324º

start at the initial side which is fixed on the positive x-axis and go counter-clockwise until you get to 324º and then go around 360º more to get an angle of 324+360=684º

start at the initial side and go clockwise until you get to the terminal side of 324º; you have made an angle of

360-324=36º and since you went clockwise the angle is negative, -36º

the angles are 684º and -36º