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F.4 Mathematics Holiday Assignment (Do them on paper)

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9. Express sin75o in surd form.

10. Solve the following equation for 0o ( x ( 360o.

(a) sinx + 2cosx = 0

(b) sin2x = cos3x

(c) cos2x + 3sinx = 3

(d) 2sinx + cosx = 1 (Hint: sin2x + cos2x ( 1)

11. Let x = 54o.

(a) Prove that cos2x + sin3x = 0

(b) Prove that sin3A = 3sinA ( 4sin3A (where A is any real number).

(c) Prove that sin54o is a root of 4y3 + 2y2 ( 3y ( 1 = 0

(d) Hence, or otherwise, express sin54o in surd form.

12. Suppose tanx and tany are roots of x2 + 2x ( 3 = 0, find the values of tan(x + y) and sin([pic]).

13. The following figure shows the graph of y = Asin(kx + () + B. Find the values of A, B, k and (.

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