a)i)Express in sin^2 x in terms of cosX.
ii) By writing cosX=Y show that the equation 7cosX + 2 - 4 sin^2 x = 0 is equivalent to 4y^2 + 7y -2 = 0.
b) Solve the equation 4y^2 + 7y -2 = 0.
c)Hence solve the equation 7 cosX + 2 - 4 sin^2X = 0, giving all solutions to the nearest 0.1(degree) in the interval 0(degree)< x < 360(degree).
Q19.A student models the evening lighting-up time by the equation L = 6.125 - 2.25cos(πt/6) where the time, L hours pm, is always in GMT ( Greenwich Mean Time) and t is in months, starting in mid-December. The model assumes that all months are equally long.
a)Calculate the value of L for mid-January and for mid-May
b)Find, by solving an appropriate equation, the two months in the year when the lighting up time will be 5pm (GMT).
c)Write down an equation for L if t were to be in months starting in mid-March.