Standard +0.3 This is a straightforward Further Maths trigonometric equation requiring knowledge of general solutions and the unit circle. Students must find where sin equals -1/2, apply the general solution formula for sine, then solve for x. While it's FP1 content, it's a standard textbook exercise with clear methodology and no novel problem-solving required, making it slightly easier than average overall.
4 Find the general solution of the equation
$$\sin \left( 4 x - \frac { 2 \pi } { 3 } \right) = - \frac { 1 } { 2 }$$
giving your answer in terms of \(\pi\).
(6 marks)
$\sin\left(-\frac{\pi}{6}\right) = -\frac{1}{2}$ | B1 | | OE; dec/deg penalised at 6th mark
$\sin\left(-\frac{5\pi}{6}\right) = -\frac{1}{2}$ | B1F | | OE; ft wrong first value
Use of $2\pi$ | M1 | | (or $n\pi$) at any stage
Going from $4x - \frac{2\pi}{3}$ to $x$ | m1 | | including division of all terms by 4
GS $x = \frac{\pi}{8} + \frac{1}{2}n\pi$ or $x = -\frac{5\pi}{24} + \frac{1}{2}n\pi$ | A1A1 | 6 marks | OE
**Total: 6 marks**
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