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What is the polar form of #( -11,24 )#?

Answer 1

Cartesian form: #(-11,24) <=> # polar form: #(sqrt(597),pi+arctan(-24/11))#

#tan(theta) = 24/(-11)#

Unfortunately, #arctan#, the inverse of #tan(theta)# is by definition an angle #in (-pi/2,+pi/2)# (i.e. in QI or Q IV)
[In the diagram above, the angle returned by #arctan(-24/11)# is shown as #theta_2#.]

Taking #arctan(24/(-11)) = arctan((-24)/11)#
gives us an angle that is "pi" radians less than the true value of #theta#

Therefore #theta = pi+arctan(-24/11)#

#(r,theta) = (sqrt(597),pi+arctan(-24/11))#

(using a calculator)
#color(white)("XXX")~~(24.4, 2.0)~~(24.4, 114.6^@)#

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Answer 2

Christopher Agresta

The polar form of (-11, 24) is 25∠116.565°.

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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.