Answers306P1^
2 (i) (a) 203 cm^2
(c) 16.9 cm^2
(ii) 19.7 cm^2
3 (i) 1.98 mm^2
(ii) 43.0 mm
5 (i) 140 yards
(ii) 5585 square yards
6 (ii) 43.3 cm
(iii) 117 cm^2 (3 s.f.)
7 (i) 62.4 cm^2
(ii) 0.65
8 (i) 43
(ii) 48 3 − 24 π
9 (i) 1.8 radians
(ii) 6.30 cm
(iii) 9.00 cm^2
10 (ii) 18 − 6 3 + 2 πActivity 7.3 (Page 245)
The transformation that maps
the curve y = sin x on to the curve
y = 2 + sin x is the translation^0
2
.In general, the curve y = f(x) + s is
obtained from y = f(x) by the
translation^0
s
.Activity 7.4 (Page 245)
The transformation that maps
the curve y = sin x on to the
curve y = sin (x − 45°) is the
translation ^450 °.In general, the curve y = f(x − t) is
obtained from y = f(x) by the
translation t
0
.Activity 7.5 (Page 246)
The transformation that maps the
curve y = sin x on to the curve
y = − sin x is a reflection in the x axis.In general, the curve y = −f(x) is
obtained from y = f(x) by a
reflection in the x axis.Activity 7.6 (Page 246)
For any value of x, the y co-ordinate
of the point on the curve y = 2 sin x
is exactly double that on the curve
y = sin x.
This is the equivalent of the curve
being stretched parallel to the y axis.
Since the y co-ordinate is doubled,
the transformation that maps the
curve y = sin x on to the curve
y = 2 sin x is called a stretch of scale
factor 2 parallel to the y axis.
The equation y = 2 sin x could also
be written as y 2 = sin x, so dividing
y by 2 gives a stretch of scale factor 2
in the y direction.
This can be generalised as the curve
y = af(x), where a is greater than 0,
is obtained from y = f(x) by a stretch
of scale factor a parallel to the y axis.Activity 7.7 (Page 247)
For any value of y, the x co-ordinate
of the point on the curve y = sin 2 x
is exactly half that on the curve
y = sin x.
This is the equivalent of the curve
being compressed parallel to the
x axis. Since the x co-ordinate is
halved, the transformation that
maps the curve y = sin x on to the
curve y = sin 2 x is called a stretch of
scale factor^12 parallel to the x axis.
Dividing x by a gives a stretch of
scale factor a in the x direction, just
as dividing y by a gives a stretch of
scale factor a in the y direction:y = f (^) ()xa corresponds to a stretch of
scale factor a parallel to the x axis.
Similarly, the curve y = f(ax), where
a is greater than 0, is obtained from
y = f(x) by a stretch of scale factor^1 a
parallel to the x axis.
Exercise 7F (Page 251)
1 (i) Translation^90
0
°
(ii) One-way stretch parallel to
x axis of s.f.^13
(^) (iii) One-way stretch parallel to
y axis of s.f.^12
(iv) One-way stretch parallel to
x axis of s.f. 2
(v) Translation^ 20
2 (i) Translation −°^600
(ii) One-way stretch parallel to
y axis of s.f.^13
(iii) Translation 10 ^
(iv) One-way stretch parallel to
x axis of s.f.^12
3 (i) (a)
(^)
(b) y = sin x
(ii) (a)
(b) y = cos x
(iii) (a)
(b) y = tan x
x
y
1
–1
O
1 3
x
y
1
–1
O
90 270
x
y
O 180