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How do you convert #r^2cos(2theta)=1# into cartesian form?

Answer 1

Benjamin Achtenberg

#x^2-y^2=1#.

The Gven Polar eqn. is #r^2cos 2theta=1#, i.e.,

#r^2cos^2 theta -r^2sin^2 theta=1#

Since, #x=rcos theta. and, y=rsin theta#, we get the cartesian eqn,

#x^2-y^2=1#.

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Answer 2

Ariana Alvarez

To convert ( r^2\cos(2\theta) = 1 ) into Cartesian form, use the double-angle identity for cosine: ( \cos(2\theta) = \cos^2(\theta) - \sin^2(\theta) ). Then substitute ( x = r\cos(\theta) ) and ( y = r\sin(\theta) ), and solve for ( x ) and ( y ). The resulting equation will be in Cartesian form.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.