The transformation P is an enlargement, centre the origin, with scale factor k, where k > 0
The transformation Q is a rotation through angle θ degrees
... [Show More] anticlockwise about the origin.
The transformation P followed by the transformation Q is represented by the matrix
−4 −4 3
M =
4 3 −4
(a) Determine
(i) the value of k,
(ii) the smallest value of θ
(4)
A square S has vertices at the points with coordinates (0, 0), (a, –a), (2a, 0) and (a, a) where a is a constant.
The square S is transformed to the square S′ by the transformation represented by M.
(b) Determine, in terms of a, the area of S′
(2)
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(Total for Question 1 is 6 marks)
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2. (a) Use the Maclaurin series expansion for cos x to determine the series expansion of
cos2 3x in ascending powers of x, up to and including the term in x4
Give each term in simplest form.
(2) (b) Use the answer to part (a) and calculus to find an approximation, to 5 decimal places, for [Show Less]