IAS -EDEXCEL

PURE MATHS 1&2

Transformation of
Trigonometric Functions

Menuka Suwinda
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9. (i)

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y = f (x)

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–2π –π O π 2π x
–1
–2
–3

Figure 3

Figure 3 shows part of the graph of the trigonometric function with equation y = f (x)
(a) Write down an expression for f (x)
(2)
On a separate diagram,
 π
(b) sketch, for –2π < x < 2π , the graph of the curve with equation y = f  x + 
 4

Show clearly the coordinates of all the points where the curve intersects the
coordinate axes.
(3)
(ii)

–2π –π O π 2π x
–1
y = g (x)

Figure 4

Figure 4 shows part of the graph of the trigonometric function with

equation y = g (x)
(a) Write down an expression for g(x)
(2)
On a separate diagram,
(b) sketch, for –2π < x < 2π , the graph of the curve with equation y = g (x) – 2
Show clearly the coordinates of the y intercept.
(2)

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6.

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O x

Figure 2

Figure 2 shows a plot of part of the curve C1 with equation

y = 5 cos x

with x being measured in degrees.

The point P, shown in Figure 2, is a minimum point on C1
(a) State the coordinates of P
(2)
The point Q lies on a different curve C2
Given that point Q
• is a maximum point on the curve
• is the maximum point with the smallest x coordinate, x > 0
(b) find the coordinates of Q when
(i) C2 has equation y = 5 cos x – 2
(ii) C2 has equation y = –5 cos x
(4)
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(Total for Question 6 is 6 marks)

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9. In this question you must show detailed reasoning.
Solutions relying entirely on calculator technology are not acceptable.

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(i) Solve, for 0  x < 360°, the equation
sin x tan x = 5
giving your answers to one decimal place.
(6)
(ii)
y

O R θ

Figure 1

Figure 1 shows a sketch of part of the curve with equation

 3 
y  A sin  2  2
 8 

where A is a constant and θ is measured in radians.

The points P, Q and R lie on the curve and are shown in Figure 1.
Given that the y coordinate of P is 7
(a) state the value of A,
(1)
(b) find the exact coordinates of Q,
(3)
(c) find the value of θ at R, giving your answer to 3 significant figures.
(4)
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Question 9 continued
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10.
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C1

P
O x

Figure 4

Figure 4 shows a sketch of part of the curve C1 with equation

 x 
y  3cos   x0
n

where n is a constant.
The curve C1 cuts the positive x-axis for the first time at point P(270, 0), as shown
in Figure 4.
(a) (i) State the value of n
(ii) State the period of C1
(2)
The point Q, shown in Figure 4, is a minimum point of C1
(b) State the coordinates of Q.
(2)
The curve C2 has equation y  2sin x  k , where k is a constant.

 12   3
The point R  a,  and the point S   a,   , both lie on C2
 5  5
Given that a is a constant less than 90
(c) find the value of k.
(2)
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(Total for Question 10 is 6 marks)

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