# Math Help - Help with this proof. Not exactly sure where to start.

1. ## Help with this proof. Not exactly sure where to start.

The statement is:

"For each real number p, there exist real numbers q and r such that qsin(r/5) = p."

We have to either prove this statement or give a counter-example.

I've been talking with others in my class and it seems like the first thing we need to do is say:

"Let p be a real number. Put r = (5/2)(pi)."

And then I plugged this in for r in the equation, getting q = p.

Is this correct? If not, what am I doing wrong? Thanks in advance for the help

2. Originally Posted by Lprdgecko
The statement is:

"For each real number p, there exist real numbers q and r such that qsin(r/5) = p."

We have to either prove this statement or give a counter-example.

I've been talking with others in my class and it seems like the first thing we need to do is say:

"Let p be a real number. Put r = (5/2)(pi)."

And then I plugged this in for r in the equation, getting q = p.

Is this correct? If not, what am I doing wrong? Thanks in advance for the help
That is exactly what I would do.

Additional note: I would start out by writing "Let q = p and r = (5/2)pi. Then...."

3. Originally Posted by undefined
That is exactly what I would do.
So, I am a little confused on what we are trying to prove. Do we need to prove that q = p or are we proving that qsin(r/5) = p?

4. Originally Posted by Lprdgecko
So, I am a little confused on what we are trying to prove. Do we need to prove that q = p or are we proving that qsin(r/5) = p?
I added an additional note to my first post, not quickly enough I guess. Let me know if it's still not clear.

5. Originally Posted by undefined
I added an additional note to my first post, not quickly enough I guess. Let me know if it's still not clear.
I see the note now. So, after setting q = p and r = (5/2)pi, then is it as simple as saying "Then, qsin(r/5) = p" or would we have to to actually plug in the values (and show that part in the proof) to prove that fact?

6. Originally Posted by Lprdgecko
I see the note now. So, after setting q = p and r = (5/2)pi, then is it as simple as saying "Then, qsin(r/5) = p" or would we have to to actually plug in the values (and show that part in the proof) to prove that fact?
I would plug in, just for clarity and to demonstrate you understand it all. Hardly takes any extra time.

7. Originally Posted by undefined
I would plug in, just for clarity and to demonstrate you understand it all. Hardly takes any extra time.
Ok, thank you so much!

8. Originally Posted by Lprdgecko
Ok, thank you so much!
You're welcome!