Thread: slope of tangent line to polar curve

1. slope of tangent line to polar curve

Find the slope of the tangent line to the polar curve for the given value of $\theta$
$r=1/\theta; \theta=2$

2. Originally Posted by vinson24
Find the slope of the tangent line to the polar curve for the given value of $\theta$
$r=1/\theta; \theta=2$
$\frac{dy}{dx}=\frac{r'(\theta)\sin\theta+r(\theta) \cos\theta}{r'(\theta)\cos\theta-r(\theta)\sin\theta}$

So in our case $\frac{dy}{dx}=\frac{-\tfrac{1}{\theta^2}\sin\theta+\tfrac{1}{\theta}\co s\theta}{-\tfrac{1}{\theta^2}\cos\theta-\tfrac{1}{\theta}\sin\theta}$

So just plug in $\theta=2$ to get your answer.