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

• Oct 5th 2010, 06:07 PM
Lprdgecko
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 :)
• Oct 5th 2010, 06:13 PM
undefined
Quote:

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...."
• Oct 5th 2010, 06:15 PM
Lprdgecko
Quote:

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?
• Oct 5th 2010, 06:17 PM
undefined
Quote:

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.
• Oct 5th 2010, 06:21 PM
Lprdgecko
Quote:

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?
• Oct 5th 2010, 06:31 PM
undefined
Quote:

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.
• Oct 5th 2010, 06:34 PM
Lprdgecko
Quote:

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!
• Oct 5th 2010, 06:37 PM
undefined
Quote:

Originally Posted by Lprdgecko
Ok, thank you so much!

You're welcome!