Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/22) | 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
calculator;

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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