The height of the tide above mean sea level on January 24 at Cape Town is modelled by

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The height of the tide above mean sea level on January 24 at Cape Town is modelled by h(t)=3sin⁡(πt6) mh(t)=3\sin\left(\frac{\pi t}{6}\right)\,\text{m}, where tt is the number of hours after midnight. (1) Graph y=h(t)y=h(t) for 0≤t≤240\le t\le24. (2) When is high tide and what is the maximum height? (3) What is the height of the tide at 2 pm? (4) A ship can cross the harbour provided the tide is at least 2 m2\,\text{m} above mean sea level. When is crossing possible on January 24?

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