One fine day in Rochester the low temperature occurs at 5 a.m. and the high temperature at 5 p.m. The temperature varies sinusoidally all day. The temperature t hours after midnight is T(t) = A + B sin where A, B, and C are certain constants. The low temperature is 47 and the high temperature is 77. Find the average temperature during the first 8 hours after noon. Hint: The high and low temperatures can be used together to find A and B. Determine C from the fact that it is hottest at 5 p.m. ("(t-C) 12

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