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The blades of a wind turbine have a diameter of 16m and rotate clockwise at a constant speed, 1 revolution every 4 seconds. The blades are fixed on a shaft such that the tips of the blades are always at least 7m above the ground. The point Q lies at the tip of one of the blades.
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Let h be the height, in meters, of Q above the ground. After t minutes, h is given by h(t)=acos(bt)+c, where a,b,c∈R and a>0.
Show that Q starts at the highest possible point.
Find the values of a, b and c.
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Find all the solutions to the equation sin2θ=√3cosθ, where 0≤θ≤2π.
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