Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2016 | Oct-Nov | (P1-9709/13) | Q#3

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Question

Showing all necessary working, solve the equation  for .

Solution

We are given equation;

We know that ; therefore,

Now we have two options.

Using calculator we can find that;

We have following properties of .

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

We utilize the periodicity property of   to find other solutions (roots) of .

Therefore;

For;

Only following solutions (roots) are within the given interval ;

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