Math questions.150 points.

Math questions.150 points.
The number of hours,H,of daylight in Madrid at paricular time of year may be approximate by H(t)=12+2.4sin[0.0172(t-80)] where t is the number of days since the start of the year.Find the average number of hours of daylight in Madrid [you may use your calculator to carry out your calculations]:a in January B in June c over a whole year d comment on the relative magnitudes of your answers to part a,b,c.why are they reasonable.
process is very important.

t\x05sin(0.0172*(t-80))\x05H(t)\x05\x05\x05t\x05sin(0.0172*(t-80))\x05H(t)
A\x051\x05-0.977612812\x059.653729251\x05\x05B\x05152\x050.945263115\x0514.26863148
\x05365\x05-0.982077623\x059.643013704\x05\x05\x05153\x050.950735535\x0514.28176528
\x053\x05-0.969797691\x059.672485541\x05\x05\x05154\x050.955926697\x0514.29422407
\x054\x05-0.965459185\x059.682897956\x05\x05\x05155\x050.960835064\x0514.30600415
\x055\x05-0.960835064\x059.693995846\x05\x05\x05156\x050.965459185\x0514.31710204
\x056\x05-0.955926697\x059.705775927\x05\x05\x05157\x050.969797691\x0514.32751446
\x057\x05-0.950735535\x059.718234715\x05\x05\x05158\x050.9738493\x0514.33723832
\x058\x05-0.945263115\x059.731368524\x05\x05\x05159\x050.977612812\x0514.34627075
\x059\x05-0.939511055\x059.745173468\x05\x05\x05160\x050.981087114\x0514.35460907
\x0510\x05-0.933481057\x059.759645464\x05\x05\x05161\x050.984271179\x0514.36225083
\x0511\x05-0.927174904\x059.774780229\x05\x05\x05162\x050.987164064\x0514.36919375
\x0512\x05-0.920594463\x059.790573288\x05\x05\x05163\x050.989764913\x0514.37543579
\x0513\x05-0.91374168\x059.807019967\x05\x05\x05164\x050.992072958\x0514.3809751
\x0514\x05-0.906618583\x059.824115401\x05\x05\x05165\x050.994087515\x0514.38581004
\x0515\x05-0.899227278\x059.841854534\x05\x05\x05166\x050.995807989\x0514.38993917
\x0516\x05-0.891569952\x059.860232116\x05\x05\x05167\x050.997233869\x0514.39336129
\x0517\x05-0.88364887\x059.879242711\x05\x05\x05168\x050.998364736\x0514.39607537
\x0518\x05-0.875466377\x059.898880696\x05\x05\x05169\x050.999200254\x0514.39808061
\x0519\x05-0.867024891\x059.919140261\x05\x05\x05170\x050.999740175\x0514.39937642
\x0520\x05-0.858326912\x059.940015412\x05\x05\x05171\x050.999984341\x0514.39996242
\x0521\x05-0.849375011\x059.961499974\x05\x05\x05172\x050.999932678\x0514.39983843
\x0522\x05-0.840171837\x059.983587591\x05\x05\x05173\x050.999585203\x0514.39900449
\x0523\x05-0.830720113\x0510.00627173\x05\x05\x05174\x050.998942018\x0514.39746084
\x0524\x05-0.821022635\x0510.02954568\x05\x05\x05175\x050.998003313\x0514.39520795
\x0525\x05-0.811082271\x0510.05340255\x05\x05\x05176\x050.996769366\x0514.39224648
\x0526\x05-0.800901963\x0510.07783529\x05\x05\x05177\x050.995240542\x0514.3885773
\x0527\x05-0.790484722\x0510.10283667\x05\x05\x05178\x050.993417293\x0514.3842015
\x0528\x05-0.779833629\x0510.12839929\x05\x05\x05179\x050.991300159\x0514.37912038
\x0529\x05-0.768951837\x0510.15451559\x05\x05\x05180\x050.988889766\x0514.37333544
\x0530\x05-0.757842563\x0510.18117785\x05\x05\x05181\x050.986186827\x0514.36684838
\x0531\x05-0.746509094\x0510.20837817\x05\x05\x05\x05averageH(t)of JUN\x0514.31773993
\x05\x05averageH(t)of JAN\x059.931053712\x05\x05\x05\x05\x05
answer of A and B as data above,I calculatd with excel.
quantion C's answer is 12 hours.
question D.because the function H(t) is a trigonometric function with period 2pie/0.0172=
365.3 and mean value 12,I believe it is reasionable.