# slope of tangent line to polar curve

#### vinson24

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

#### chiph588@

MHF Hall of Honor
Find the slope of the tangent line to the polar curve for the given value of $$\displaystyle \theta$$
$$\displaystyle r=1/\theta; \theta=2$$
$$\displaystyle \frac{dy}{dx}=\frac{r'(\theta)\sin\theta+r(\theta)\cos\theta}{r'(\theta)\cos\theta-r(\theta)\sin\theta}$$

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

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

vinson24