Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2010  OctNov  (P29709/22)  Q#5
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Question
Solve the equation , giving all solutions in the interval .
Solution
We are given;
We know that ;
Let , then we can write;
Now we have two options.





Since ;


We know that except where or undefined, therefore;






Using calculator we can find that;


Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


We utilize periodicity property of to find other solutions in the given interval .
For;















Only solutions of the given equation within given interval are;








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