trigonometric functions given at each
question. Use the information given in
the figure to determine the values of
the unknown variables :
2.1 The graph of y = a sin k(x + p)
2.2 The graph of y = a cos k(x + p)
2.3 The graph of y = a sin k(x + p)
2.4 The graph of y = a cos k(x + p)
2.5 The graph of y = a sin k(x + p)
2.6 The graph of y = a cos k(x + p)
and g(x) = c + sin dx for −180° ≤ x ≤ 180°
are shown.
4.1 Determine the values of a, b, c and d
by using the graphs. [ A 4.1 ]
4.2 Calculate the value of f(x) if x = 0° without
using a calculator. [ A 4.2 ]
4.3 Determine x by using the graphs if
4.3.1 g(x) = 2 [ A 4.3.1 ]
4.3.2 f(x) ≥ g(x) [ A 4.3.2 ]
4.4 The Y-axis is translated to pass
through the turning point of f,
where f(x) reaces a maximum.
Determine an equationfor f in
the form y = . . . with reference to
the new set of axes. [ A 4.4 ]
and g(x) = sin cx for −90° ≤ x ≤ 90°
are shown.
5.1 Determine the values of a, b and c
by using the graphs. [ A 5.1 ]
5.2 Use the graphs to answer the
following questions :
5.2.1 Write down the range of f. [ A 5.2.1 ]
5.2.2 For what values of x is f(x)
decreasing as x increases? [ A 5.2.2 ]
5.2.3 If x ∈ [−90° ; 0°], for what values
of x is f(x).g(x) ≥ 0? [ A 5.2.3 ]
5.3 If x ∈ [−90° ; 90°], solve the equation
cos (x − 30°) = sin x and hence
write down the values of x in the
interval [−90° ; 90°] for which g(x) > f(x).
[ A 5.3 ]
5.4 The graph of h(x) is formed by
translating the graph of g(x) 60° to
the left. Wrire down the equation
of h(x). [ A 5.4 ]
5.5 How can the graph of f(x) be
translated to form the graph of g(x)?
[ A 5.5 ]
and g(x) = c sin dx for −120° ≤ x ≤ 90°
are shown.
6.1 Write down the amplitude and
period of g. [ A 6.1 ]
6.2 Determine the values of a, b, c
and d. [ A 6.2 ]
6.3 Write down the range of g. [ A 6.3 ]
6.4 Write down the value(s) of x < 0°
for which f(x).g(x) ≥ 0. [ A 6.4 ]
6.5 If the Y-axis is moved to the left so
as to pass through the point of
intersection of the given cosine curve
and the X-axis, which function is now
represented by the curve that initially
represented the given sine function?
[ A 6.4 ]
and g(x) = sin (x + b) are drawn for the
interval −180° ≤ x ≤ 90°
7.1 Write down the value of b. [ A 7.1 ]
7.2 Write down the period of g. [ A 7.2 ]
7.3 Write down the value(s) of x in
the interval − 180° ≤ x ≤ 90° for
which f(x) − g(x) = 0 [ A 7.3 ]
7.4 For which values of x in
the interval − 180° ≤ x ≤ 90°
7.4.1 is sin (90° − x) > g(x)? [ A 7.4.1 ]
7.4.2 is f(x).g(x) < 0? [ A 7.4.2 ]
7.4.3 is f(x).g(x) ≥ 0? [ A 7.4.3 ]
7.5 The graph of h is obtained by shifting
f 3 units upwards. Determine the range of h.
[ A 7.5 ]
7.6 The graph of p is obtained by shifting
f 3 units downwards. Write down the
equation of p. [ A 7.6 ]
7.7 The graph of q is obtained by shifting
f 30° to the left. Write down the
equation of p. [ A 7.7 ]
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