Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2005 | Oct-Nov | (P1-9709/01) | Q#1

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Question

Solve the equation , for .

Solution

We have;

We need to express the equation in terms of single trigonometric ratio;

We have the trigonometric identity;

We can write it as;

Hence the equation becomes;

To solve this equation for , we can substitute . Hence,

Now we have two options;

Since;

Using calculator we can find the values of .

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

Symmetry
Property

Hence;

For

For

Therefore, we have four solutions (roots) of the equation;

To find all the solutions (roots) of  we utilize the periodic property of .

Periodic
Property

or

Therefore;

For

For

For

For

For

Hence all the solutions (roots) of the equation  within  interval are;

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