Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 2 (P29709/02)  Year 2012  OctNov  (P29709/22)  Q#8
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Question
i. Given that and find in terms of .
ii. Solve the equation
giving all solutions in the interval 0^{◦} ≤ x ≤ 360^{◦}.
Solution
i.
We are given;
We are given that ; therefore;
ii.
We are required to solve giving all solutions in the interval 0^{◦} ≤ x ≤ 360^{◦}.
Therefore;
Let , then;
Now we have two options.





Since ;




Using 



Now we find all solutions in the interval 0^{◦} ≤ x ≤ 360^{◦}.
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 ;




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