頁二第張四第日九初月十年酉己屆夏

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日八十月一十年九六九一圈公年八十五國民華中 育教僑華

小學學位供應

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收費低庭的官立、韋貼】大〇年,宫#小舆與私 區人口分佈情况,拇設 助學位的護會。在一配激育的勃發毆, 一之目染,是按照它九各,逐座齡兒童均有狳得資,成爲一個見產所必備 ,俄府经较小学浟育 小學計劃,使每一個心|臂在本港將页日趨普遍

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至能 在官民兩方積極推行下 預計明年

臀訂製多年來努力推 大資助小學的計劃,經 〇年時,其對此將爲百。生 助教育的機會。 四十八,但到了一九七|多中學學位與小學畢業

據估計:由政府

的資制小學學位,到

·三間電子公司職員獲得

大等

翻瘾,的,必普部

菜可以發政小備温愛 學

Solutions for Exercise.

(a) L.S. = (tan • →

2. cosec

按記

|摘牌小學兒選所

的成就,可從為去女生 .敎臂司署在此方面

來官改小準的謠得以

堅道書院獎學金

名後公佈 新珊定下月開課 第二批名單將於廿一日止報

毎年僭艿煙五蔴個。」示對傩子工業設置低導

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做工

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及种麼。

「爲「保讓你的眼睛。. 【傳主題爲原則在失前两月,即已由教臂可知及市政署預光邀約,以便說個 除,每像可由二十至四十人組成,所唱歌曲詞語,但須自行撰作,均以宜 參加比賽學校分中學組及小學組,舒壓亲世用英文叫中文唱出之歌唱 年主不同,如以往之「牙齒健康』及各祉保俪問題,一九六九年度之主 此項健浟歌唱比瘲象辦已有多年,今年參加者更崑赜際,歌唱比筷喂,

院旅,造

170英文中學會考試題預習專欄

Circular

堅道英文書院主編

數學科

MATHEMATICS (3)

letions of the "General Angle. The general...

angle is an angle of any size including negative angles.

ve

008 (90°-

rdinate of P

tan(90°

sin(90° COB (90°

Bin

coto

90:-0

9040

M

(ii) 90° + 0.

-ve

Lot OX, Or be the usual perpendicular axes used in . graphical work, and let the same scales be used along the axes of x and of y.

If Pbe the point (x,y) OP - D (alvays positive) and:/POX , the following are the definitions of the trigonometrio functions when ✪ is the general angle,

ain e = z

⚫008

It is to be noted that the position Of can be arrived at by turning through any number of complete turns plus the angle &, and all positive angles are obtained by tuaning in an anti-clookwise direction. from OX, and negative angles by turning in a clockwise direction from OXS

The signs of the circular fumotions of e in the four quadrants XOY, X'OT, X'OT', XOY" (first, second third and fourth quadranta respectively) are obtained in the following table. Quadrant = y = sine f coed " tent =

lat

2nd

3rd

+

·

*

+

*r and / F2OX - 90° -

From congruent triangldm and the fact that lios in the second quadrant, #ip(90° + 0)

coo(90°

tan(goo.

co-ordinate of

ordinate of P.

A

(tane

2 sec 9

tan o cosec e - 2 coseo §.

2 tan @ corec@

+ 1 – 2860M.

- act ̃0 - 2000

COS 1 sin ✪ cos

8000- 2. cat 0 aad

~ 2 00sec ℗ – (cot 9 - 800 0) —

(5) L.§. - (1 + sinle + com 8)

2

1 + sin ê + 008 + 2x1a 0 4 2 cos

+ 2 sin 8 com e

2 + 2 sin � 2008 0.

2(1 + sin @ + COM • sin & convă

► 2(1 + sin 8)(1 + con 6)

~2(1 +

-tan

sao Đại hạn Đ

Bec

pectan

2sece tan b secetan ✪

Sin(90° Cos(90°

2 COR

co.t

- sec - tan

(iii)—Xvii) The following is a summary of

results established

cos (1800

sin(1800)

-sine

Bin(180°)

cos(180°

tan(1800 - e) - -tan 0

tan(180°

sin(270°

Bin(2700

QOB(270°

COR(270°

tan(2700 *)

·cot

tan(270°

sin(360°)

cos(360 - 0)

tan(3 360

Bin(-9) cos (~ 0) tan(-

#in

-tas

tan 07

+

sa tan ✪ -:

B8:00 -

tan 0-2 gdo a' tan d

seo ̈e - tan

From the right-angled triangle as shown

COB

To remember these results it is advisable to follow the diagram, using the word cast' showing. what funotions are positive in the varioue quadrants

- tan, o cor

(a

The signs for Gobec 6, seo 0,

cote can be obtained from. the table being the same as for X

sin Boost, tàn 0

respectively, since they are the invarade of these functions.

5

Since the position OP is unaltered if any multiple of 27 radians be added or subtracted from the general angle, it follows that any multiple of 27 radians (3600) can be added to or subtracted from the angle of a trigonometrio function without altering its value, Example: Find

(1)

win 792° (ii) ten (-3369), using tables. Bin 792o - sin (7920 2 - 3600) - min 720 0.95106

· tan 240 0.44523 tan (-3360) - tan(−3360 + 3600)

To find the sins,“ sosine, and tangent of the angles

(1) 900 — e (11) 900

(iv) 180° + @ {v}

(vii) 360°

(i) 90°

(111) 1809 -0

e(vi) 2700 +

OPF

* = /P ̧0X - 90°

From congruent triangles #in(90° - 0)

y co-ordinats of F

Bxample. Find the aine, cosine and tangent of the

angles (1) 150° (11) 2559 (iii) 295° (iv) -1400:

.

(i) sin(150°) - ain(180° 30°) = sin 30°

COS (150°)

008 (1800

tan(1500)

30%)

tan(180-30)

tan30

=

75 -0.9659 -0.2588

3.7320

-0.9063 0.4226.

4. (三) 8 adn

Using sin

88 cos

= -2.1445

(11) sin(255°) - sin(180 + 75°)

cos(255°) = cos(180°+75°).

C0875 tan(255°) - tan(180 +75°) = tan75°

(111) sin(295°) - sin(360°~65°) - -Bin65

008(295°) - cos(360°-65° COB 650 tan(2950) = tan(360°-65?) -

=

(iv) sin(-140°)- -Bin140° - -sin(180°-40°)

008(-140°)

--P.6428

cos1400 cos (180-40)

-0.7660

-tan1400 -tan(180°-40°) tan400 0.8391

Exercise

1. Find the galue of

(a) 4c030 sin 270° -

tan 45

(b) 3 sino sec180°

Find from the tables the sine, cosine and tangent. of the following anglest

(a) -20° (b) -110° (c) 410° (a).930° (e) -210%

sin d

q sin d

9-1

8 0092 @ -

6.

1 ➡ 00520,

the equation becomes,

+ 6 cos 0 - 9 = 07

cos + 1 =0

(2 con @ -1){4 com 0 − 1)

COB O

COR

75°

(11) 2 seo?

Tsing se

1+ 3 tan

- 1 + tan 8, the equation become

2 + 2 tan 8.

1+ 3 tan

(2 tan

¥ 3 ten +

1)(tan ✪ − 1) = 0

or

45° or e-

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