Alex C.

asked • 09/17/17

Identify the curve by finding a cartesian equation for the curve

r2sin(2x)=1

Arturo O.

Alex,
 
Could there by a typo in the problem statement?  Could the given equation really be
 
r2 sin(2θ) = 1 
 
instead of
 
r2 sin(2x) = 1 ?
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09/17/17

Alex C.

Hi, yes there was a typo. It is meant to be angle thetha.
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09/18/17

Arturo O.

Alex,
 
Thank you for the update.  Ira gave you a good solution for angle θ.
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09/18/17

1 Expert Answer

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Ira S. answered • 09/17/17

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First, use the double angle formula for sin to get sin 2x = 2(sinx)( cos x).
Then you can separate the r2 and rewrite your equation as 
2(rsinΘ)(rcosΘ) =1
 
Now, x=rcosΘ and y = rsinΘ
 
So your equation becomes 2xy=1 or xy=1/2....a type of hyperbola.
 
Hope this helped
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Arturo O.

Ira,
 
If the given equation was
 
r2 sin(2θ) = 1,
 
then your solution is right on.  But as stated, the equation is
 
r2 sin(2x) = 1
 
If
 
x = r cosθ
y = r sinθ,
 
we end up with 
 
r2 [2 sin(r cosθ) cos(r sinθ)] = 1
 
I suspect a typo in the problem statement.  Please see my other comment.  What do you think?
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09/17/17

Ira S.

I took it as a typo.
 If it wasn't a typo, r2 = x2 + y2 and you could just replace this in the original equation to get
(x2 + y2)sin(2x) =1.......and that would be it...not very interesting.
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09/17/17

Arturo O.

Certainly not an easily recognizable figure!
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09/17/17

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