| Date | None Specimen | Marks available | 4 | Reference code | SPNone.1.sl.TZ0.6 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Hence or otherwise and Solve | Question number | 6 | Adapted from | N/A |
Question
The expression \(6\sin x\cos x\) can be expressed in the form \(a\sin bx\) .
Find the value of a and of b .
[3]
a.
Hence or otherwise, solve the equation \(6\sin x\cos x = \frac{3}{2}\) , for \(\frac{\pi }{4} \le x \le \frac{\pi }{2}\) .
[4]
b.
Markscheme
recognizing double angle M1
e.g. \(3 \times 2\sin x\cos x\) , \(3\sin 2x\)
\(a = 3\) , \(b = 2\) A1A1 N3
[3 marks]
a.
substitution \(3\sin 2x = \frac{3}{2}\) M1
\(\sin 2x = \frac{1}{2}\) A1
finding the angle A1
e.g. \(\frac{\pi }{6}\) , \(2x = \frac{{5\pi }}{6}\)
\(x = \frac{{5\pi }}{{12}}\) A1 N2
Note: Award A0 if other values are included.
[4 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 3 - Circular functions and trigonometry » 3.5 » Solving trigonometric equations in a finite interval, both graphically and analytically.
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