a. Express 1.4 sin 5.6 cos in the form R sin ( ), where R and
a. Express 1.4 sin θ − 5.6 cos θ in the form R sin (θ − α), where R and α are constants, R > 0 and 0 < α < 90°. Round R and α to 3 decimal places.
b. Hence find the maximum value of 1.4 sin θ − 5.6 cos θ and the smallest positive value of θ for which this maximum occurs.
The length of daylight, d(t) at a location in northern Scotland can be modelled using the equation
where t is the numbers of days into the year.
c. Calculate the minimum number of daylight hours in northern Scotland as given by this model.
d. Find the value of t when this minimum number of daylight hours occurs.
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