The temperature inside Vanessa's house hours after midday is given by .

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

Problem

The temperature inside Vanessa's house

t

hours after midday is given by

T(t)=6\sin\left(\frac{\pi}{12}t\right)+26\,\text{°C}

. (1) Sketch the graph of

T

against

t

for

0\leq t\leq24

. (2) Find the temperature inside Vanessa's house at midnight. (3) Find the temperature inside Vanessa's house at

2\,\text{pm}

. (4) Find the maximum temperature inside Vanessa's house and the time at which it occurs.