Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2012 | Oct-Nov | (P1-9709/13) | Q#6

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Question

The functions  and  are defined for  by

Solve the following equations for .

     i.       , giving your answer in terms of .

   ii.       , giving your answers correct to 2 decimal places.

Solution


i.
 

We have the functions;

We write as;

We are given that;

Therefore;


ii.
 

We have the functions;

We write as;

We are given that;

Therefore;

We utilize the symmetry property of   to find other solutions (roots) of :

Symmetry
Property

Hence;

For ;

Therefore, all the solutions of  within  are;

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