Question

Letx(t) = t - sin(t) and y(t) = 1 - cos(t); Att = 6

Answer 1

Given;

`\begin{gathered} x(t)=t-\sin(t) \\ \\ y(t)=1-\cos(t) \\ \\ t=6 \end{gathered}`
`\begin{gathered} x(6)=6-\sin(6) \\ \\ x(6)=5.90 \end{gathered}`
`\begin{gathered} y(6)=1-\cos(6) \\ \\ y(6)=0.01 \end{gathered}`

Then;

`\begin{gathered} (dx)/(dt)=1-\cos(t) \\ \\ t=6; \\ \\ (dx)/(dt)|_(t=6)=1-\cos(6) \\ \\ (dx)/(dt)|_(t=6)=0.01 \end{gathered}`
`\begin{gathered} (dy)/(dt)=\sin(t) \\ \\ t=6; \\ \\ (dy)/(dt)|_(t=6)=\sin6 \\ \\ (dy)/(dt)|_(t=6)=0.10 \end{gathered}`
`\begin{gathered} (dy)/(dx)=(dy)/(dt)/(dx)/(dt) \\ \\ (dy)/(dx)=(\sin(t))/(1-\cos(t)) \\ \\ (dy)/(dx)|_(t=6)=(\sin(6))/(1-\cos(6)) \\ \\ (dy)/(dx)|_(t=6)=19.08 \end{gathered}`
`\begin{gathered} speed=√((1-\cos t)^2+(\sin t)^2) \\ \\ speed=√(1-2\cos t+\cos^2t+\sin^2t) \\ \\ speed=√(2-2\cos t) \\ \\ t=6; \\ \\ speed=√(2-2\cos(6)) \\ \\ speed=0.10 \end{gathered}`