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How do you convert #y = -x# into polar form?

Answer 1

Violet Anderson

Polar form of #y=-x# is #theta=(3pi)/4#

The relation between polar coordinates #(r,theta)# and Cartesian coordinates #(x,y)# is given by

#x=rcostheta#, #y=rsintheta# and #r^2=x^2+y^2#

As such #y=-x# can be written as

#rsintheta=-rcostheta# or

#(rsintheta)/(rcostheta)=-1# or

#tantheta=-1=tan((3pi)/4)# or

#theta=(3pi)/4#

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Answer 2

Quinn Anderson

To convert the equation ( y = -x ) into polar form, we can use the relations between Cartesian coordinates (x, y) and polar coordinates (r, θ).

In polar coordinates, ( x = r \cos(\theta) ) and ( y = r \sin(\theta) ).

Given ( y = -x ), substitute ( -x ) for ( y ) in the polar coordinate equation:

[ -x = r \sin(\theta) ]

Now, we have the equation in terms of ( r ) and ( \theta ).

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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.