# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2013 | Oct-Nov | (P1-9709/13) | Q#7

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Question

a)   Find the possible values of for which , giving your answers correct to 3 decimal places.

b)  Solve the equation for giving in terms of in your answers.

Solution

a)

We have; We can rearrange the equation as; We know that; Therefore we can write above equation as;     b)

To solve the equation for , let Since given interval is , for interval can be found as follows; Multiplying the entire inequality with 2;  Adding in the entire inequality;  Since ; Hence the given interval for is .

Therefore we can write the given equation as;  Using calculator we can find the value of . We utilize the symmetry property of to find another solution (root) of : Symmetry Property or Hence;  For ;  Therefore, we have two solutions (roots) of the equation;   To find all the solutions (roots) of the we utilize the periodic property of . Periodic Property or Hence  For For    For             Hence all the solutions (roots) of the equation for interval are;   Since                Hence all the solutions (roots) of the equation for are;  