Standard +0.3 This is a straightforward application of the product rule and double angle formula to find stationary points. While it requires differentiation of a product of trigonometric functions and solving the resulting equation, these are standard P3 techniques with no novel insight required. The question is slightly above average difficulty due to the algebraic manipulation needed after differentiation, but remains a routine textbook-style problem.
4 A curve has equation \(y = \cos x \sin 2 x\).
Find the \(x\)-coordinate of the stationary point in the interval \(0 < x < \frac { 1 } { 2 } \pi\), giving your answer correct to 3 significant figures.
Obtain correct derivative in any form, e.g. \(-\sin x \sin 2x + 2\cos x \cos 2x\)
A1
Use double angle formula to express derivative in terms of \(\sin x\) and \(\cos x\)
M1
Equate derivative to zero and obtain an equation in one trig function
M1
Obtain \(3\sin 2x = 1\), or \(3\cos 2x = 2\) or \(2\tan 2x = 1\)
A1
Solve and obtain \(x = 0.615\)
A1
## Question 4:
| Answer | Mark | Guidance |
|--------|------|----------|
| Use correct product rule | M1 | |
| Obtain correct derivative in any form, e.g. $-\sin x \sin 2x + 2\cos x \cos 2x$ | A1 | |
| Use double angle formula to express derivative in terms of $\sin x$ and $\cos x$ | M1 | |
| Equate derivative to zero and obtain an equation in one trig function | M1 | |
| Obtain $3\sin 2x = 1$, or $3\cos 2x = 2$ or $2\tan 2x = 1$ | A1 | |
| Solve and obtain $x = 0.615$ | A1 | |
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4 A curve has equation $y = \cos x \sin 2 x$.\\
Find the $x$-coordinate of the stationary point in the interval $0 < x < \frac { 1 } { 2 } \pi$, giving your answer correct to 3 significant figures.\\
\hfill \mbox{\textit{CAIE P3 2020 Q4 [6]}}