8
\includegraphics[max width=\textwidth, alt={}, center]{6025cf1d-525e-4f12-9517-f20ef5fff2fa-3_698_1006_758_571}
The diagram shows the curve with parametric equations
$$x = \sin t + \cos t , \quad y = \sin ^ { 3 } t + \cos ^ { 3 } t$$
for \(\frac { 1 } { 4 } \pi < t < \frac { 5 } { 4 } \pi\).
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = - 3 \sin t \cos t\).
- Find the gradient of the curve at the origin.
- Find the values of \(t\) for which the gradient of the curve is 1 , giving your answers correct to 2 significant figures.