9709 P33 - Nov 2011 - Q8
1632
The diagram shows the curve with parametric equations
\(x = \\sin t + \\cos t, \quad y = \\sin^3 t + \\cos^3 t,\)
for \(\frac{1}{4}\pi < t < \frac{5}{4}\pi.\)
(i) Show that \(\frac{dy}{dx} = -3 \sin t \cos t.\)
(ii) Find the gradient of the curve at the origin.
(iii) Find the values of \(t\) for which the gradient of the curve is 1, giving your answers correct to 2 significant figures.
