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How do you convert r = -2cos(θ) – 2sin(θ) into cartesian mode?

Answer 1

Elias Ackerman

#x^2+y^2=-2x-2y#

Remember that:

#r^2=x^2+y^2#

#rcos(theta)=x#

#rsin(theta)=y#

We have:

#r=-2cos(theta)-2sin(theta)#

Note here that we are just missing the #r#.

Multiply both sides by #r#.

#=>r^2=-2rcos(theta)-2rsin(theta)# We can now substitute.

#=>x^2+y^2=-2x-2y#

You can simplify this from here on, depending on what your teacher wants. (Turn this to a circle relation #(x-h)^2+(y-k)^2=r^2#)

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Answer 2

Sophie Adams

To convert the polar equation ( r = -2\cos(\theta) - 2\sin(\theta) ) into Cartesian mode, use the trigonometric identities ( x = r\cos(\theta) ) and ( y = r\sin(\theta) ). Substitute these into the equation and simplify to obtain the Cartesian equation.

( r = -2\cos(\theta) - 2\sin(\theta) )

( x = -2\cos(\theta) )

( y = -2\sin(\theta) )

( x = -2x )

( y = -2y )

( x^2 + y^2 = 4(x^2 + y^2) )

( 3x^2 + 3y^2 = 0 )

( x^2 + y^2 = 0 )

( x = 0 ) and ( y = 0 )

The Cartesian equation of the polar equation ( r = -2\cos(\theta) - 2\sin(\theta) ) is ( x^2 + y^2 = 0 ).

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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.