Solving Trigonometric Equations

[eutas1]

I don't understand their final answer?
(Refer to attachment)

 

[Steven G]

What do you mean by cycle or 2nd cycle??

 

[eutas1]

What do you mean by cycle or 2nd cycle??

For sine and cos graphs, one cycle is 2pi. However for tan, one cycle is pi.

In relation to the 2nd circle: since tan's cycle is pi, this means it is within the first two quadrants. But in the worked solution (attachment), they use -(pi/3) which would be in the 4th quadrant --> which is in the 2nd cycle.

Sorry if this doesn't make sense