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Date May 2008 Marks available 3 Reference code 08M.1.sl.TZ1.2
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 2 Adapted from N/A

Question

Let p=sin40 and q=cos110 . Give your answers to the following in terms of p and/or q .

Write down an expression for

(i)     sin140 ;

(ii)    cos70 .

[2]
a(i) and (ii).

Find an expression for cos140 .

[3]
b.

Find an expression for tan140 .

[1]
c.

Markscheme

(i) sin140=p     A1     N1

(ii) cos70=q     A1     N1

[2 marks]

a(i) and (ii).

METHOD 1

evidence of using sin2θ+cos2θ=1     (M1)

e.g. diagram, 1p2 (seen anywhere)

cos140=±1p2     (A1)

cos140=1p2     A1     N2

METHOD 2

evidence of using cos2θ=2cos2θ1     (M1)

cos140=2cos2701     (A1)

cos140=2(q)21 (=2q21)     A1     N2

[3 marks]

b.

METHOD 1

tan140=sin140cos140=p1p2     A1     N1

METHOD 2

tan140=p2q21     A1     N1

[1 mark]

c.

Examiners report

This was one of the most difficult problems for the candidates. Even the strongest candidates had a hard time with this one and only a few received any marks at all.

a(i) and (ii).

Many did not appear to know the relationships between trigonometric functions of supplementary angles and that the use of sin2x+cos2x=1 results in a ± value. The application of a double angle formula also seemed weak.

b.

This was one of the most difficult problems for the candidates. Even the strongest candidates had a hard time with this one and only a few received any marks at all. Many did not appear to know the relationships between trigonometric functions of supplementary angles and that the use of sin2x+cos2x=1 results in a ± value. The application of a double angle formula also seemed weak.

c.

Syllabus sections

Topic 3 - Circular functions and trigonometry » 3.3 » The Pythagorean identity cos2θ+sin2θ=1 .

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