 Solution

ID: 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/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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