Chapter(^7)
305
P1^
(vii) (^12)
(viii) 23
(ix) − 1
5 (i) −60°
(ii) −155.9°
(iii) 54.0°
6 (i)
(ii) (a) False
(b) True
(c) False
(d) True
7 (i) α between 0° and 90°, 360°
and 450°, 720° and 810°,
etc. (and corresponding
negative values).
(ii) No: since tan α = siconsαα, all
must be positive or one
positive and two negative.
(iii) No: sin α = cos α ⇒ α = 45°,
225°, etc. but tan α = ±1 for
these values of α, and
sin α = cos α = 1
2
8 (i) 5.7°, 174.3°
(ii) 60°, 300°
(iii) 116.6°, 296.6°
(iv) 203.6°, 336.4°
(v) 0°, 90°, 270°, 360°
(vi) 90°, 270°
(vii) 0°, 180°, 360°
(viii) 54.7°, 125.3°, 234.7°, 305.3°
(ix) 60°, 300°
(x) 18.4°, 71.6°, 198.4°, 251.6°
9 A: (38.2°, 0.786),
B: (141.8°, −0.786)
10 (ii) x = 143.1° or x = 323.1°
11 (ii) x = 26.6° or x = 206.6°
12 (ii) θ = 71.6° or θ = 251.6°
13 θ = 90° or θ = 131.8°
Exercise 7D (Page 238)
1 (i) π 4
(ii) π 2
(iii) 23 π
(iv) 512 π
(v) 53 π
(vi) 0.4 rad
(vii) 52 π
(viii) 3.65 rad
(ix) 56 π
(x) 25 π
2 (i) 18°
(ii) 108°
(iii) 114.6°
(iv) 80°
(v) 540°
(vi) 300°
(vii) 22.9°
(viii) 135°
(ix) 420°
(x) 77.1°
3 (i) (^12)
(ii) 3
(iii) 3
2
(iv) − 1
(v) − 1
(vi) 23
(vii) 3
(viii) –^1
2
(ix) 12
(x) (^12)
4 (i) ππ 6 ,^116
(ii) ππ 4 ,^54
(iii) ππ 4 ,^34
(iv) 76 ππ,^116
(v) 34 ππ,^54
(vi) ππ 3 ,^43
5 (i) 0.201 rads, 2.940 rads
(ii) −0.738 rads, 0.738 rads
(iii) −1.893 rads, 1.249 rads
(iv) −2.889 rads, −0.253 rads
(v) −1.982 rads, 1.982 rads
(vi) −0.464 rads, 2.678 rads
6 0 rads, 0.730 rads, 2.412 rads,
rads
●^?^ (Page^ 241)
Draw a line from O to M, the mid-
point of AB. Then find the lengths
of OM, AM and BM and use them to
find the areas of the triangles OAM
and OBM, and so that of OAB.
In the same way,
AB = AM + MB = 2AM.
Exercise 7E (Page 241)
1
r (cm) θ (rad) s (cm) A (cm^2 )
5 4 54 ^258
8 1 8 32
4 12 2 4
112 3 2 38
5 45 4 10
1.875 0.8 1.5 1.41
3.46^23 7.26 4
y
0
shaded areas are congr uent
–90 180 360
1
–1
x
(180 – x)
y = sin x
x