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How do you graph #r=-8cos2theta#?

Answer 1

Dylan Arnold

See 8-like graph and details.

#r = -8 cos 2theta in [ - 8, 8 ], # with period #( 2pi )/2 = pi#

No pixels for # < 0#

#rArr 2theta in [ pi/2, 3/2pi ] U [ 5/2pi, 7/2pi]#

# rArr theta in [ pi/4, 3/4pi ] U [ 5/4pi, 7/4pi]#. So,

in two periods #theta in [ 0, 2pi ]#.

Use

0 <= r = sqrt ( x^2 + y^2 ) and ( x, y ) = r ( cos theta, sin theta )# d

convert to

#( x^2 + y^2 )^ 1.5 = - 8 (x^2 - y^2 )#, using

#cos 2theta = cos^2theta - sin ^2theta )#

The Socratic 8-like graph is immediate. graph{ ( x^2 + y^2 )^ 1.5 + 8 (x^2 - y^2 ) = 0[ -18 18 -9 9 ]}

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Answer 2

Carter Anderson

To graph the polar equation ( r = -8\cos(2\theta) ), follow these steps:

Plot points for various values of ( \theta ).
Substitute each value of ( \theta ) into the equation to find the corresponding value of ( r ).
Use the polar coordinate system, where ( r ) represents the distance from the origin and ( \theta ) represents the angle from the positive x-axis.
Plot each point with its corresponding ( r ) value at the angle ( \theta ).
Connect the plotted points to form the graph of the 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.