Standard +0.3 This is a standard harmonic form question requiring routine application of R sin(x - α) = R sin x cos α - R cos x sin α, matching coefficients to find R = 2 and α = π/6, then using knowledge that sin has maximum value 1 at π/2. All steps are textbook procedures with no novel problem-solving required, making it slightly easier than average.
7 Express \(\sqrt { 3 } \sin x - \cos x\) in the form \(R \sin ( x - \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { 1 } { 2 } \pi\). Express \(\alpha\) in the form \(k \pi\).
Find the exact coordinates of the maximum point of the curve \(y = \sqrt { 3 } \sin x - \cos x\) for which \(0 < x < 2 \pi\).
So they are interchangeable and therefore there is no unique solution
E1
Part (ii):
Answer
Marks
Guidance
Answer/Working
Mark
Guidance
The missing symbols form a \(3 \times 3\) embedded Latin square.
M1
There is not a unique arrangement of the numbers 1, 2 and 3 in this square.
E1
Total: [18]
## Question 7:
**Part (i):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| There are neither 3s nor 5s among the givens. | M1 | |
| So they are interchangeable and therefore there is no unique solution | E1 | |
**Part (ii):**
| Answer/Working | Mark | Guidance |
|---|---|---|
| The missing symbols form a $3 \times 3$ embedded Latin square. | M1 | |
| There is not a unique arrangement of the numbers 1, 2 and 3 in this square. | E1 | |
**Total: [18]**
7 Express $\sqrt { 3 } \sin x - \cos x$ in the form $R \sin ( x - \alpha )$, where $R > 0$ and $0 < \alpha < \frac { 1 } { 2 } \pi$. Express $\alpha$ in the form $k \pi$.
Find the exact coordinates of the maximum point of the curve $y = \sqrt { 3 } \sin x - \cos x$ for which $0 < x < 2 \pi$.
\hfill \mbox{\textit{OCR MEI C4 2008 Q7 [6]}}