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Math 20 - Calculus I $4.2 - Extra Credit Applied Project: The Calculus of Rainbows Show your work! Good luck! (40pts) Rainbow
TUULUVOSE 3.4 The figure below shows that the angle of elevation from the observer up to the highest point on the rainbow is
tomorrowly Taking k = show that the minimum deviation is about 129° and so the rainbow angle for the secondary rainbow is abo
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1Equation D(a) + q [having quantities a, b ] D(a) = (a - b) + (1 - 2B) + (a - b) D(a) = 180 + 20 - 4B sin a Sink +e (used equaD(a) + f (used function | D(a) = 180 + 2a-4 Lot 06) = ca [ 18020 – asin sima) + [used result derivative of sin^-1(xl 4cosa+ e [used equation | D(a) = 0 4 cosa 2. VR-sina 50 4(k? - sin?a) = 16 cosa k? - sin’a = 4(1 - sinʼa) 3 sin’a = 4 - k + a [ wi+ sina [used equation - =k sin P= sin (sina) B = sin -11 +e (with specific amount a_m = 59.4 B-sin (sin 59,4) B =40.21° D(a

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