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Date May 2008 Marks available 6 Reference code 08M.2.hl.TZ1.7
Level HL only Paper 2 Time zone TZ1
Command term Solve, Express, and Hence Question number 7 Adapted from N/A

Question

A system of equations is given by

cosx+cosy=1.2

sinx+siny=1.4 .

(a)     For each equation express y in terms of x.

(b)     Hence solve the system for 0<x<π, 0<y<π .

Markscheme

(a)     y=arccos(1.2cosx)     A1

y=arcsin(1.4sinx)     A1

 

(b)     The solutions are

x = 1.26, y = 0.464     A1A1

x = 0.464, y = 1.26     A1A1

[6 marks]

Examiners report

The majority of candidates obtained the first two marks. Candidates who used their GDC to solve this question did so successfully, although few candidates provided a sketch as the rubric requires. Attempts to use “solver” only gave one solution.

Some candidates did not give the solutions as coordinate pairs, but simply stated the x and y values.

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.6 » Algebraic and graphical methods of solving trigonometric equations in a finite interval, including the use of trigonometric identities and factorization.
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