Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry

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7  The function f is such that f(x) = a − b cos x for 0°  x  360°, where a and

b are positive constants. The maximum value of f(x) is 10 and the minimum

value is −2.

(i) Find the values of a and b.

(ii) Solve the equation f(x) = 0.

(iii) Sketch the graph of y = f(x).

[Cambridge AS & A Level Mathematics 9709, Paper 1 Q5 November 2008]

8  The diagram shows the graph of y = a sin(bx) + c for 0  x  2 π.

(i) Find the values of a, b and c.

(ii) Find the smallest value of x in the interval 0  x  2 π for which y = 0.

[Cambridge AS & A Level Mathematics 9709, Paper 1 Q4 June 2009]

9  The function f is defined by f : x  5 − 3 sin 2 x for 0  x  π.

(i) Find the range of f.

(ii) Sketch the graph of y = f(x).

(iii) State, with a reason, whether f has an inverse.

[Cambridge AS & A Level Mathematics 9709, Paper 12 Q4 November 2009]

10  The function f : x  4 – 3 sin x is defined for the domain 0  x  2 π.

(i) Solve the equation f(x) = 2.

(ii) Sketch the graph of y = f(x).

(iii) Find the set of values of k for which the equation f(x) = k has no solution.

The function g : x  4 − 3 sin x is defined for the domain^12 π  x  A.

(iv) State the largest value of A for which g has an inverse.

(v) For this value of A, find the value of g–1(3).

[Cambridge AS & A Level Mathematics 9709, Paper 12 Q11 June 2010]

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