Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2012  OctNov  (P29709/21)  Q#3
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Question
Solve the equation , for .
Solution
We are required to solve;
Therefore;
We have the trigonometric identity;
Let , then;
Since , therefore;
Using calculator we can find that;
Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 






We utilize the periodicity/symmetry property of to find other solutions (roots):
But it is evident that all other values obtained will lie outside the desired range .
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