Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / 6 / a

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- Solution a

Solution

The maximum of sine is one. The allowed parameter values giving

sin (3 t) = 1

are

t = \frac{π}{6}, \frac{5 π}{6}, \frac{3 π}{2} .

Substituting each into

x = cos t

gives

y_{m a x} = 1, x \in {\frac{3}{2}, - \frac{3}{2}, 0} .

All three parameter values lie in the original interval, so none of these maxima is discarded.

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