Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | 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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