Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2012 | Oct-Nov | (P2-9709/21) | Q#3

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  Question

Solve the equation , for .

Solution

We are required to solve;

Therefore;

We have the trigonometric identity;

Let , then;

Since , therefore;

Using calculator we can find that;

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

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

But it is evident that all other values obtained will lie outside the desired range .

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