Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | May-Jun | (P1-9709/11) | 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
Property

 

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
Property

or

 

Therefore;

 

For

For

 

For;

 

 

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

 

 

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