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How do you convert #r - 2 cos t = 3 sin t# to rectangular form?

Answer 1

#x^2+y^2-2x-3y=0#

Relation between polar coordinates #(r,t)# and rectangular coordinates is given by #x=rcost#, #y=rsint#, #r^2=x^2+y^2# and #tant=y/x#.

Hence multiplying each term in #r-2cost=3sint# by #r#

#hArrr^2-2rcost=3rsint# or

#x^2+y^2-2x=3y# or

#x^2+y^2-2x-3y=0#

graph{x^2+y^2-2x-3y=0 [-4.313, 5.69, -1.38, 3.62]}

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Answer 2

Abigail Armstrong

To convert ( r - 2 \cos(t) = 3 \sin(t) ) to rectangular form, we use the relationships between polar and rectangular coordinates:

( x = r \cos(t) ) ( y = r \sin(t) )

Substitute these relationships into the given polar equation:

( r - 2 \cos(t) = 3 \sin(t) )

( x - 2x = 3y )

( x - 3y = 0 )

This is the rectangular form of the polar equation.

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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.