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Question Number 90099 by Rio Michael last updated on 21/Apr/20

given the polar equation

r = a^{2} \sin 2 θ show the tangents at

the poles of this polar equation is .

θ = {\frac{π}{4}, \frac{3 π}{4}, \frac{5 π}{4}, \frac{7 π}{4}}

Commented by jagoll last updated on 21/Apr/20

\frac{dr}{d θ} = {2 a}^{2} \cos 2 θ = 0

\cos 2 θ = \cos \frac{π}{2}

2 θ = \pm \frac{π}{2} + 2 k π

θ = \pm \frac{π}{4} + k π

{\begin{cases} θ = \frac{π}{4} + k π \Rightarrow θ = {\frac{π}{4}, \frac{5 π}{4}} \\ θ = - \frac{π}{4} + k π \Rightarrow θ = {\frac{3 π}{4}, \frac{7 π}{4}} \end{cases}

Commented by Rio Michael last updated on 21/Apr/20

but sir why did you differentiate when we know that at the poles,

r = 0 ?