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Verifying a Reduction Formula In Exercises 79-82, use
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Calculus of a Single Variable
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- Meteorology The normal monthly hightemperatures H (in degrees Fahrenheit) in Erie,Pennsylvania, are approximated byH(t) = 57.54 − 18.53 cos πt6 − 14.03 sin πt6and the normal monthly low temperatures L areapproximated byL(t) = 42.03 − 15.99 cos πt6 − 14.32 sin πt6where t is the time (in months), with t = 1 correspondingto January (see figure). (Source: NOAA)1 2 3 4 5 6 7 8 9 10 11 1220406080Month of yearTemperature(in degrees Fahrenheit)tL(t)H(t)(a) What is the period of each function?(b) During what part of the year is the difference betweenthe normal high and normal low temperaturesgreatest? When is it least?(c) The sun is northernmost in the sky around June 21,but the graph shows the warmest temperaturesat a later date. Approximate the lag time of thetemperatures relative to the position of the sun.arrow_forwardCalculus Evaluate there integral using a rationalizing substitution [² dx/(x² + x√√x)arrow_forwardSin(2x)Cos(nx) daarrow_forward
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