Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2010  OctNov  (P29709/23)  Q#6
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Question
i. Express in the form , where and , giving the exact value of R and the value of correct to 2 decimal places.
ii. Hence solve the equation
Giving all solutions in the interval .
Solution
i.
We are given the expression;
We are required to write it in the form;
If and are positive, then;
can be written in the form
can be written in the form
where,
and , , with
Considering the given equation, we have following case at hand;
can be written in the for
Comparing it with given equation Therefore


Therefore;
Finally, we can find , utilizing the equation;
Using calculator we can find that;
Therefore;
ii.
We are required to solve the equation;
As demonstrated in (i), we can write;
Therefore, we need to solve;
Using calculator we can find that;
We utilize the symmetry property of to find another solution (root) of :
Properties of 

Domain 

Range 

Odd/Even 

Periodicity 



Translation/ Symmetry 






Hence;
Therefore;
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