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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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