Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2005  OctNov  (P19709/01)  Q#1
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Question
Solve the equation , for .
Solution
We have;
We need to express the equation in terms of single trigonometric ratio;
We have the trigonometric identity;
We can write it as;
Hence the equation becomes;
To solve this equation for , we can substitute . Hence,
Now we have two options;











Since;
Using calculator we can find the values of .




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


Symmetry 

Hence;
For 
For 




Therefore, we have four solutions (roots) of the equation;




To find all the solutions (roots) of we utilize the periodic property of .


Periodic 
or

Therefore;




For 
For 
For 
For 








For





























Hence all the solutions (roots) of the equation within interval are;


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