Past Papers’ Solutions  Cambridge International Examinations (CIE)  AS & A level  Mathematics 9709  Pure Mathematics 1 (P19709/01)  Year 2017  MayJun  (P19709/13)  Q#5
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Question
(i) Show that the equation may be expressed as
.
(ii) Hence solve the equation for 0^{o} < < 180^{o}.
Solution
(i)
We are given that;
Utilizing ;
(ii)
We are required to solve the equation for 0^{o} < < 180^{o}.
From (i) we know that given equation can be written as;
Now we have two options.


Using calculator; 



Properties of 

Domain 

Range 

Periodicity 



Odd/Even 

Translation/ Symmetry 


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


For;





Only following solutions (roots) are within the given interval 0^{o} < < 180^{o}.


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