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X. Pages 37–39. (1) (2) 90.

(3) 44. (4) 17. (5) 112} ft. (6) 571 ft. (7) 93 ft, (8) 838000 miles. (9) } radian=611 degrees. (10) 2141 degrees. (11) 51,4". (12) about 34 yds. (13) 1:3.1416. (14) 3.1416. (15) 3.1418. (16) 400 : 1. (17) •0000484.... (18) 4941 in. (19) i.e. a right angle. (21) 473 : 489.

180 (22) (i) k=1, (ü) k=

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150%,

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XI. Pages 4043. (1) 10° (2) 33°, 150.

(3) 90°, 45°. (4) 189, 2210 (5) 38°, 18o. (7) 45°, 60°, 75o. (8) 39°, 60°, 81o. (9) 30°, 60°, 90° (14) 25°, 8° 6'.

(15) 11 25

37 (16) 10800

(17)
(i) 120°, 133-38,

(ii) 135°,
3

& 135 (iii) 1569, 173-35,

(20) 450'. (21) (1) 34, (ii)

10ac (22) 18 (23) a right angle. (24)

96 9a + 106

57

57 9. (25) degrees. (26)

(27) 10c

9

19 38 2 1800T

T2 (28)

(29) 197 + 1800

(30) 9 or 16. 107 + 18000

15

15.

27

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XII. Pages 50–52. (1) (i) DA, BD. (ii) DB, AD. (iii) DA, CD. (iv) DC, AD. DB DC

CD

DA DB (2) (i) (ii) (iii) (iv) AB CA"

BA

(v)

AD
DC
CD
DA
BD

DA
(vi) (vii)
AC: CA

(viii) (ix)
CD

(x)
BA

CA

.

AD

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CB ,

DB BA CD CB

DB BA (3) (i) CB' CA

(ü)

CA

(ii)

CD' CB
DB BC AD AB

DB BC (iv)

(v)
AB'

(vi)
AB'AC: AD' AB

· AC

BA

or

AC:

DA
AC DC

AB
(4) (i) (ii) or
BA
EA EC:

( (iii)
BC

(iv)

AE
AD AB

BD

DB BA AE (v)

(vi) (vii) or AB

or
BO

CD CB CA
DA
AC DC

DB BC
(viii) (ix) or
BD

or EB

(x) EA

(xi)
BD

AB AC
BE
AE'

BA

(5) sin A= }, cos A =$, tan A=; sin B=$, cos B=, tan B=s. (7) Of the smaller angle, the sine=1's, cosine=1}, tangent=is. Of the larger angle, the sine=1}, cosine=is, tangent=*.

1 (8) Of the smaller angle, the sine = $, cosine= vå, tangent of the larger angle, the sine=V3

vos

, cosine = }, tangent=v3.

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XIV, Pages 63–65. (1) 179 ft. (2) 346 ft. (3) 86.6 ft. (4) 138.5 ft. (5) 71 ft. (6) 60°, 173 ft. (7) 63:17 yds. (8) 34.15 ft. (9) 73.2 ft. (10) 86.6 ft. (11) •866 miles=1524 yds. (12) 173.2 yds. (14) 373 ft. (15) 3733 ft.

V6 (16) miles = 6465 ft.

13. (17)

(18) 300,

36 (19) about 523.6 miles.

XVI. Page 74.

1 - cos? A
sin A=71- cosA, tan A=

cos A
cot A=
COS A

Vi- cosĀ' 1

1 sec AS

cosec A

1- cos À 1 cot A

1
cOS A =

tan d
1+cot A Ji+cot? A cot A'

J1+cot: A
sec A=

cosec A=V1+ cot? A. cot A

(1)

CO3 A'

(2)

sin A=

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sec? A - 1

1 cOS A=

tan A= sec A -1, sec A

sec A
1

sec A
cosec A=
sec? A -1° '

sec? A - 1

cot A=

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cot A-V1 – sin? À

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1
cosec” A - 1

1
(4) sin A=
cos A=

tan A=
cosec A
cosec A

cosec A - 19 cot A=cosec- A -1, seo A =

cosec A cosec? A -1

sin A (5) Cos A=V1 - sino Ā, tan A=

11- sin’ A

sin A 1

1 Bec A=

cosec A= 1-sinA'

sin A tan A

1

1 (6) sin A=

cos 4 =

cot A= V1+tan? A

1+tan’ A

J1+tan’ A sec A=V1+tano Ā, cosec A=

tan A

tan A'

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XVII. Page 75.

2/2 1 (1) , $. (2)

3

(3) $ g.

2./2 1 113

13
(4)

15
(5)
15

(6)
b

6 (7)

(8)
Nc2_62

a+62
Na- 1 1
(9)

(11) hm (1+ka)=1.
u-1

XVIII. Page 77.
(2) sec increases continuously from 1 to 0.
(3) sin A diminishes continuously from 1 to 0.
(4) cot diminishes continuously from co to 0.

XIX. Page 82.
(4) Yes.
(5) No.

(6) Yes.
(7). (i) 60°. (ii) - 100°, (iii) 00. (iv) - 260°.

21
(vi) 410°. (vii)

4.

)

3

(v) 1150.

XX. Page 84.

(1) 450.
(5) 30°.

(2) 30°. (6) 30°.

(3) 450
(7) 30°.

(4) 60°.
(8) 09, or 450.

(9) 90°, or 60°.
(13) 90°, or 45°.
(17) 30°.

(10) 600
(14) 18o.
(18) 300.

(11) 450.
(15) 45°.

(12) 45° (16) 45°.

XXI. Page 85. (3) the value 3 is inadmissible. (4) (5) 1, or 1. (6) 4, or .

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(7) the value is inadmissible. (9) 1-sin4 0.

6 (10) 1-3 sin? 0+3 sin4 0.

1-2 cosa 0+2 cos4 0 (11)

cost @ 1-sind (13)

1+sin A (14) cosec o decreases continuously from co to 1. (15) cot increases continuously from 0 to 0.

)

XXII. Tage 89. (1) +6. (2) 0. (3) +2. (4) +3. (5) +10. (6) 0. (7) +7. (8) +7.

XXIV. Page 94. (1) The second. (2) The fourth. (3) The second. (4) The third. (5) The fourth. (6) The first. (7) The second. (8) The first. (9) The first. (10) The fourth. (11) The fourth. (12) The first, if n be even, the third, if n be odd.

XXV. Page 98. (1) +, +, +. (2)

t,

(3)
-,t,
(5) +,

(6)

-, -, +. (7) +,

(8) +,+,+, (9) +, +, to (10) +, +, +. (11) +, -,

(12)

-, t,
XXVI. Page 100.
1

1 1 (1) +1,

13:
(2) +

- 1.
2

V2 V2
V3

1
}, -V3. (4) -4, +

73

+.

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XXVII. Page 100. Each of these expressions changes continuously as the angle A increases from 0° to 360°, and their values are repeated at each com. plete revolution of the revolving line.

Their values are given below when they are zero and when they cease to increase and begin to decrease, and vice versa. The first table gives also the sign of each between the values.

00
900

1180° |27001

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The following figures exhibit the changes in the sign and magni. tude of sin 0 (fig. i.), cos 0 (fig. ii.), and tan 0 (fig. iii.). The measure of the distance from 0 along the line OX=the circular measure of the angle; the vertical distance from 0X measures the Ratio.

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