A curve ${C}$ has parametric equations $x={{t}^{3}}+2t$, ${x = t^3 + 2t, \quad y = 5\sin t}$ where $

Question

A curve ${C}$ has parametric equations $x={{t}^{3}}+2t$, ${x = t^3 + 2t, \quad y = 5\sin t}$ where ${0 \leq t \leq \frac{3\pi}{2}}$. Sketch ${C}$, indicating all axial intercepts and endpoints. The line ${y = 1 - x}$ intersects the curve ${C}$. Find the point(s) of intersection.

Accepted Answer

Axial intercepts $(0,0)$ and $(\pi^3+2\pi,0)$, endpoint $\left(\left(\dfrac{3\pi}{2}\right)^3+3\pi,-5\right)$ Intersection $(0.288,0.711)$

EJC Graphing Techniques Tutorial Q2

EJC Graphing Techniques Tutorial Q2

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