Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2018  MayJun  (P29709/22)  Q#7
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Question
i. Show that
ii. Solve the equation for , giving your answers correct to 3 significant figures.
iii. Find
Solution
i.
We are given;
provided that
provided that
ii.
We are required to solve the equation for .
As demonstrated in (i);
Therefore;
Let ;
Now we have two options.




Since ; 





Using calculator; 



Now we find all solutions in the interval ^{.}
Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


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




For ;




Only following solutions (roots) are within the given interval ;
iii.
We are required to find;
As demonstrated in (i);
Therefore;
Hence;
Rule for integration of is:
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