Chapter 10 - Parametric And Polar Curves; Conic Sections - 10.3 Tangent Lines, Arc Length , And Area For Polar Curves - Exercises Set 10.3 - Page 726: 2

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$\dfrac{dy}{dx}=\dfrac{dy/d \theta }{dx/d \theta }\\=\dfrac{r \cos \theta+\sin\theta \dfrac{dr}{ d \theta}}{- r \sin \theta+\cos\theta \dfrac{dr}{ d \theta}}$ Now, $\dfrac{dy}{dx}=\dfrac{(1) \cos (\dfrac{\pi}{2})+\sin (\pi/2) (-1)}{(-1) \sin (\dfrac{\pi}{2})+\cos (\pi/2) (-1) }\\=1$