Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2016  MayJun  (P19709/11)  Q#2
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Question
Solve the equation for .
Solution
We are given;
We have the trigonometric identity;
From this identity we can have;
Substituting in given equation;
Let ;
Now we have two options.











Since;
Using calculator we can find the values of .



NOT POSSIBLE

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


Symmetry 

Hence;
For ;
Therefore, we have two solutions (roots) of the equation;


To find all the solutions (roots) over the interval , we utilize the periodic property of for both these values of .


Periodic 
or

Therefore;




For 
For 




For;















Hence all the solutions (roots) of the equation for are;


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