O-LevelAdditional MathematicsTrigonometry4037/21 · May/June 2016 · Q98 Marks

Given that y = atan bx + c has period π/4 radians and passes through the points (0, -2) and (π/16, 0), find the value of each of the constants a, b and c.

(a)Given that y = atan bx + c has period π/4 radians and passes through the points (0, -2) and (π/16, 0), find the value of each of the constants a, b and c.[3]
(b)(i)On the axes below, draw the graph of y = 2 cos 3x + 1 for -2π/3 ≤ x ≤ 2π/3 radians. [Figure 9(b)(i) showing empty axes with x-axis marked from -2π/3 to 2π/3 and y-axis from -4 to 4][3]
(b)(ii)Using your graph, or otherwise, find the exact solutions of (2 cos 3x + 1)² = 1 for -2π/3 ≤ x ≤ 2π/3 radians.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[B3] a=2 b=4 c=-2 B1 for each correct value
[B3,2,1,0] sinusoidal curve symmetrical about y-axis clear intent to have amplitude of 2 2 cycles If not fully correct max B2
[B2] -2π/6, -π/6, π/6, 2π/6 cao B1 for any 4 correct

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