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How do you find the points of intersection of #r=3(1+sintheta), r=3(1-sintheta)#?

Answer 1

Christopher Agresta

Hence the points of interaction are:

# (3, sin npi) #

If we consider the interval #[0.2pi)# this gives two polar coordinates:

# (3, 0) # and # (3, pi) #

We have:

# r = 3(1+sintheta) #
# r = 3(1-sintheta) #

At any point of intersection both equations are simultaneously satisfied, so we have:

# 3(1+sintheta) = 3(1-sintheta) #
# :. 1+sintheta = 1-sintheta #
# :. 2sintheta = 0 #
# :. sintheta = 0 #
# :. theta = npi #

And with #sintheta=0# we have

# r = 3(1+0) #
# :. r =3 #

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Answer 2

Evelyn Agard

To find the points of intersection of the polar curves ( r = 3(1 + \sin(\theta)) ) and ( r = 3(1 - \sin(\theta)) ), set the two equations equal to each other and solve for ( \theta ). Once you find the values of ( \theta ), plug them back into either equation to find the corresponding values of ( r ). These pairs of ( r ) and ( \theta ) will represent the points of intersection.

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Answer from HIX Tutor

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