Trigonometry Question: Dealing with Negative and Positive Values for Theta

[Samurai44]

In trigonometry equation (finding theta):
1) If the range of theta includes negative and positive part (such as -360<=theta<=360), and I got a value of 90,180,270 or 360.. Do I have to write the answer twice positive and negative?

2) if range of theta is positive only, and I got a negative value of theta, do I have to do 360 + (negative value of theta)? .. To make the answer positive

 

[BvU]

1) no, all $\theta$ are in range (but see comment (*))
2. yes, repeatedly if necessary (you may find $\theta$ = -3000) -- the wording here is confusing: -120 would have to be reported as -120 + 360 = 240.

(*)
Make a drawing of the unit circle. $-360 \le \theta\le +360$ seems unlogical. Could it be $-180 < \theta \le 180$ ?

 

[Samurai44]

1) no, all $\theta$ are in range (but see comment (*))

(*)
Make a drawing of the unit circle. $-360 \le \theta\le +360$ seems unlogical. Could it be $-180 < \theta \le 180$ ?

But suppose the range is -180<=theta<=180
If i got a value of 90 or 180, would it be + and negative?

For the -360<=theta<=360 it's like two ranges : one is from 0 to 360, the other from 0 to -360, so two drawings.. Or maybe I have to write -360<=2theta<=360

 

[BvU]

But suppose the range is -180<=theta<=180
If i got a value of 90 or 180, would it be + and negative?

The 90 is positive and 90 - 360 is out of range. So +90 only.
The 180 is on the bound. Your bounds coincide, so both -180 and +180 are in range. But there is only one answer, so the overlapping bounds are not a good idea. That's why I used $-180 < \theta \le 180$.

 

[Samurai44]

The 90 is positive and 90 - 360 is out of range. So +90 only.
The 180 is on the bound. Your bounds coincide, so both -180 and +180 are in range. But there is only one answer, so the overlapping bounds are not a good idea. That's why I used $-180 < \theta \le 180$.

But consider this graph, isn't it possible to write -90?

 

[BvU]

In your case 1) the 270 is in range.
In your case 2) the 90 is in range and remains 90. The 270 is over range and comes in range by subtracting 360. In that sense -90 is one of the answers.

If i got a value of 90 or 180, would it be + and negative?

Perhaps I read this question in your post #3 in a different way than you intended.

To summarize:

case 1) 0, 90, 180, 270
case 2) 0, 90, 180, -90​