find all solutions of tan 5x =-1
The two possible answers are
-pi/20 + pi/5n=x
-pi/4+pin=x

I know the second is false because it doesnt divide pi by 5, however Im wondering what makes -pi/20 a more valid answer.
invtan(-1)=5*-pi/20, why does it not also produce -pi/4

Question

find all solutions of tan 5x =-1
The two possible answers are 
-pi/20 + pi/5n=x
-pi/4+pin=x

I know the second is false because it doesnt divide pi by 5, however Im wondering what makes -pi/20 a more valid answer. 
invtan(-1)=5*-pi/20, why does it not also produce -pi/4

anonymous · Answer

$$\tan(5x)=-1$$
$$\tan(5x)=\tan(-45)$$
$$5x = -45+180k$$
$$x=-9+36k$$
$$x=27^{o}+36k$$

anonymous · Answer

That's how we solve them here, maybe it will answer your question.