Why doesn't -2 count as an answer?

[pope4]

I was doing this question, which requires you to solve the question and give a general solution in radians, and I understand how to factor it and everything. However, I'm a bit confused as to why the -2 doesn't count as an answer. Is it because of some unspecified domain, even though the question doesn't give one?

 

[Steven G]

Yes, 2 + SinB = 0 when SinB=-2. The problem is the Sine of NO angles equals -2!!
The sine of an angle is ALWAYS between -1 and 1. Note that 2 is not between -1 and 1

 

[Dr.Peterson]

I was doing this question, which requires you to solve the question and give a general solution in radians, and I understand how to factor it and everything. However, I'm a bit confused as to why the -2 doesn't count as an answer. Is it because of some unspecified domain, even though the question doesn't give one?

View attachment 34563

I'd call it a range issue: -2 is not in the range of the sine.

But did you try to do the work you thought should have been done? If you had tried solving [imath]2+\sin(B)=0[/imath], you would have answered your own question!

And if it had been a domain issue (e.g. if you had found [imath]B=\frac{\pi}{2}[/imath] as a "solution" to a slightly different equation), you would have discovered it when you checked your answer and found that one side of the equation was undefined.

These are two very important ways to learn: Do the thing you are unsure of rather than just asking others, and check any answer you get to make sure it makes sense.

 

[pope4]

I'd call it a range issue: -2 is not in the range of the sine.

But did you try to do the work you thought should have been done? If you had tried solving [imath]2+\sin(B)=0[/imath], you would have answered your own question!

And if it had been a domain issue (e.g. if you had found [imath]B=\frac{\pi}{2}[/imath] as a "solution" to a slightly different equation), you would have discovered it when you checked your answer and found that one side of the equation was undefined.

These are two very important ways to learn: Do the thing you are unsure of rather than just asking others, and check any answer you get to make sure it makes sense.

I wholeheartedly admit, that was my bad! I tried checking it but instead of taking the inverse of sin, I took sin(-2) and got an answer and rushed to ask questions. I'll make sure to be more thorough next time!

 

[Dr.Peterson]

I wholeheartedly admit, that was my bad! I tried checking it but instead of taking the inverse of sin, I took sin(-2) and got an answer and rushed to ask questions. I'll make sure to be more thorough next time!

Ah! Yet another example of why we ask you to show whatever work you've done, rather than just ask a question. That can save a lot of time when there's just a silly mistake to catch.

 

[Steven G]

There really is no reason to try to compute inverse sin (-2) as you should know that it doesn't exist. If you rely on calculators or online software you'll not see that there is no answer. Your brain is much smarter than a computer. Sin x and Cos x are between -1 and 1.