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Question Number 87130 by jagoll last updated on 03/Apr/20

$$\mathrm{find}\mathrm{the}\mathrm{slope}\mathrm{for}\mathrm{the}\mathrm{curve}$$$$\mathrm{r}=3\sin 2\theta \mathrm{at}\theta =\frac{\pi }{4}?$$

Commented by mr W last updated on 03/Apr/20

$$y=r\sin \theta =3\sin 2\theta \sin \theta$$$$x=r\cos \theta =3\sin 2\theta \cos \theta$$$$\frac{dy}{dx}=\frac{dy}{d\theta }\times \frac{1}{\frac{dx}{d\theta }}=\frac{\sin 2\theta \cos \theta +2\cos 2\theta \sin \theta }{-\sin 2\theta \sin \theta +2\cos 2\theta \cos \theta }$$$$=\frac{1\times \frac{\sqrt{2}}{2}+2\times 0\times \frac{\sqrt{2}}{2}}{-1\times \frac{\sqrt{2}}{2}+2\times 0\times \frac{\sqrt{2}}{2}}=-1$$

Commented by mr W last updated on 03/Apr/20

Commented by john santu last updated on 03/Apr/20

$$\mathrm{sir}\mathrm{joggal}.\mathrm{do}\mathrm{you}\mathrm{mean}\mathrm{the}\mathrm{curve}$$$$\mathrm{in}\mathrm{polar}\mathrm{coordinate}?$$

Commented by jagoll last updated on 03/Apr/20

$$\mathrm{yes}\mathrm{mister}\mathrm{john}$$

Commented by jagoll last updated on 03/Apr/20

$$\mathrm{thank}\mathrm{you}\mathrm{mr}\mathrm{w}$$

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