Moderate -0.3 This is a straightforward trig equation requiring knowledge of the general solution formula and special angle values. While it's Further Maths (FP1), it only involves applying sin⁻¹(√3/2) = π/3 and the standard general solution sin(θ) = k gives θ = nπ + (-1)ⁿα, then solving for x. It's slightly easier than average due to being a direct application with a special angle and no algebraic manipulation needed.
6 Find the general solution of the equation
$$\sin \left( 2 x - \frac { \pi } { 2 } \right) = \frac { \sqrt { 3 } } { 2 }$$
giving your answer in terms of \(\pi\).
One value of $2x - \frac{\pi}{2} = \frac{\pi}{3}$ | B1 | OE (PI); degrees/decimals penalised in 6th mark only
Another value is $\pi - \frac{\pi}{3} = \frac{2\pi}{3}$ | B1F | OE (PI); ft wrong first value
Introduction of $2n\pi$ or $n\pi$ | M1 |
General solution for $x$ | m1 |
GS: $x = \frac{5\pi}{12} + n\pi$ or $x = \frac{7\pi}{12} + n\pi$ | A2,1 | OE; A1 if one part correct
**Total: 6 marks**
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