# Question- LO3: Use analytical and computational methods for solving problems by relating sinusoidal wave and vector functions to their respective engineering applications. a- A system of solar panels produces a daily average power P that changes during the …

sinusoidal wave and vector functions to their respective engineering applications. a Asystem of solar panels produces a daily average power P that changes during the year. It is maximum on the 21* of June (day with the highest number of daylight) and equal to 20 kwh/day. We assume that P varies with the time t according to the sinusoidal function P(t) = a cos [b(t - d)] +c, where t = 0 corresponds to the first of January, P is the power in kwh/day and P(t) has a _period of 365 days (28 days in February). The minimum value of Pis 4 kwhiday. 1- Find the parameters a, b, ¢ and d. 2. Sketch P(t) over one period from t = 0 to t= 365. 3- When is the power produced by the solar system minimum?. 4 The power produced by this solar system is sufficient to power a group of machines if the power produced by the system is greater than or equal to 16 kwh/day. For how many days, ina year, is the power produced by the system sufficient? The figure shown in the diagram below is showing a heavy box which is suspended by two wires where OA is T1 and OB is T2. Represent the two forces T1 and T2 by their vector ‘components using the directions given in the diagram. ‘The two forces shown in the diagram below show two forces F1 and F2 and their values are 20Ib and 30Ib respectively. These two forces act on an object P as shown in the figure. What is the resultant force acting on the object?

ec f g Find the angle between the vectors P = 4i + 0] + 7k and Q = -2i +) + 3k. Using the formula for compound angles prove that sin (x — Tr), sin (x +) and cos (x += )are all the same. ‘Analyze the components of the expression and compare it to the analytical values Evaluate the compound angle expression sin (a + b ) if the angles a and b are obtuse angles and with the following values: Sin a = 3 and b =33.

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