Target Mathematics

3.40: Stationary point and equation for 3sin2x2cosx3\sin^{2}x - 2\cos x

0606/22/M/J/22 — Question 8 · 10 marks

The function ff is defined by f(x)=3sin2x2cosxf(x) = 3\sin^{2}x - 2\cos x for π2x3π2\dfrac{\pi}{2} \leqslant x \leqslant \dfrac{3\pi}{2}, where xx is in radians.
(a)
Find the xx-coordinate of the stationary point on the curve y=f(x)y = f(x).
[5]
(b)
Solve f(x)=13cosxf(x) = 1 - 3\cos x.
[5]