# Tangent and concavity of parametric equations

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###### Lessons

- Find $\;\frac{dy}{dx}\;$ and $\;\frac{d^2y}{dx^2}$
**Questions Regarding to Tangents and Concavity**

Find the tangent to the cycloid $x=r(\theta - \sin \theta)$, $y=r(1-\cos \theta)$ when $\theta = \frac{\pi}{4}$ and $r$ > $0$. Determine the concavity for all values of $\theta$. (Do not eliminate the parameter)- Find the point of the parametric curve $x=t^2+1$ and $y=t^3+t^2$, in which the tangent is horizontal.
- Find the tangent to the curve $x=3 \cos t$, $y=4 \cos t$ by: