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Date May 2015 Marks available 3 Reference code 15M.1.sl.TZ1.5
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 5 Adapted from N/A

Question

Given that \(\sin x = \frac{3}{4}\), where \(x\) is an obtuse angle,

find the value of \(\cos x;\)

[4]
a.

find the value of \(\cos 2x.\)

[3]
b.

Markscheme

valid approach     (M1)

eg\(\;\;\;\), \({\sin ^2}x + {\cos ^2}x = 1\)

correct working     (A1)

eg\(\;\;\;{4^2} - {3^2},{\text{ }}{\cos ^2}x = 1 - {\left( {\frac{3}{4}} \right)^2}\)

correct calculation     (A1)

eg\(\;\;\;\frac{{\sqrt 7 }}{4},{\text{ }}{\cos ^2}x = \frac{7}{{16}}\)

\(\cos x =  - \frac{{\sqrt 7 }}{4}\)     A1     N3

[4 marks]

a.

correct substitution (accept missing minus with cos)     (A1)

eg\(\;\;\;1 - 2{\left( {\frac{3}{4}} \right)^2},{\text{ }}2{\left( { - \frac{{\sqrt 7 }}{4}} \right)^2} - 1,{\text{ }}{\left( {\frac{{\sqrt 7 }}{4}} \right)^2} - {\left( {\frac{3}{4}} \right)^2}\)

correct working     A1

eg\(\;\;\;2\left( {\frac{7}{{16}}} \right) - 1,{\text{ }}1 - \frac{{18}}{{16}},{\text{ }}\frac{7}{{16}} - \frac{9}{{16}}\)

\(\cos 2x =  - \frac{2}{{16}}\;\;\;\left( { =  - \frac{1}{8}} \right)\)     A1     N2

[3 marks]

Total [7 marks]

b.

Examiners report

Many candidates were able to find the cosine ratio of \(\frac{{\sqrt 7 }}{4}\) but did not take into account the information about the obtuse angle and seldom selected the negative answer. Finding \(\cos 2x\) proved easier; the most common error seen was \(\cos 2x = 2\cos x\).

a.

Many candidates were able to find the cosine ratio of \(\frac{{\sqrt 7 }}{4}\) but did not take into account the information about the obtuse angle and seldom selected the negative answer. Finding \(\cos 2x\) proved easier; the most common error seen was \(\cos 2x = 2\cos x\).

b.

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.3 » Double angle identities for sine and cosine.
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