Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2017 | May-Jun | (P1-9709/13) | Q#5

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Question

(i)          Show that the equation  may be expressed as

.

(ii)        Hence solve the equation  for 0o < < 180o.

Solution

(i)
 

We are given that;

Utilizing ;

(ii)
 

We are required to solve the equation  for 0o < < 180o.

From (i) we know that given equation can be written as;

Now we have two options.

Using calculator;

 

Properties of

Domain

Range

Periodicity

Odd/Even

Translation/

Symmetry

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

Periodicity

For;

Only following solutions (roots) are within the given interval 0o < < 180o.

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