Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  OctNov  (P19709/13)  Q#3
Question
Showing all necessary working, solve the equation for .
Solution
We are given equation;
We know that ; therefore,
Now we have two options.






Using calculator we can find that; 



We have following properties of .
Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


We utilize the periodicity property of to find other solutions (roots) of .
Therefore;
For;















Only following solutions (roots) are within the given interval ;




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