Solving Trigonometric Equations

[eutas1]

Why do they use n = -1 and n = 0 for the first three positive solutions?

I thought n was the number of cycles? So wouldn't the first three positive solutions be n = 1, n = 2 and n = 3 ????

(Refer to attachment A)

 

[Steven G]

Obviously you are wrong. When n = -1, the angles is positive! Plug in n=-2 and you'll that the angle is negative.

13+12n >0
12n>-13
n>-13/12
Since -1>-13/12, we can have n=-1 and get a positive answer

 

[eutas1]

Obviously you are wrong. When n = -1, the angles is positive! Plug in n=-2 and you'll that the angle is negative.

13+12n >0
12n>-13
n>-13/12
Since -1>-13/12, we can have n=-1 and get a positive answer

Oh, I see now that if you just plug in n = -1, you would get a POSITIVE answer. But, isn't 'n' = the number of cycles? So would that mean n = -1 is one cycle backwards, n = 0 means no cycles (original), and n = 1 means one cycle after???

 

[Steven G]

Stop thinking cycles!
There is no 1st cycle as the values of n has no starting value and no finishing value.
If you think that I am wrong then tell me what the 1st value for n is.

 

[eutas1]

Stop thinking cycles!
There is no 1st cycle as the values of n has no starting value and no finishing value.
If you think that I am wrong then tell me what the 1st value for n is.

I will stop thinking in cycles! That's where all the issues came from with some of my other questions as well.. Thank you so much!