寶四第五集
日三十月一十年午丙曆食
WAH KIU YAT PO
英文中學會考試題預習專欄
數學科
fu Tot #
(+) ·歐陽鎰文·
MATHEMATICS (10)
Ratios of angles of any magnitude, 'Sine & Cosine formulae for a s
LESSON TO
The trigonometrical ratios of 9, for a pt P. Qré defined as
**
Sin &
4- coord, of p
OP
PM OP
CAC BE }
SK
дри PM
IT
COS =
X=Coard. of P.
OM
OP I
OP
ор
Case OM
tan 6 = 3-comed at p
PM
#AM
cator:
-coord. oP
OM 1058 PM
a
with centre 0; and fixed radius of let a circle be des cribed, then, the diameters x'x, YY' divide the circh into 4 quadrants If P. P2. P. and Pq are the position
of P in the four quadrants.
as shown, then it will be seen that (NOTE: the radius, which only fixes the
always regarded as positive)
boundary of the angle,
(+) In the 15t
رشی
quadrant
85
-
All lines are t've
-'n, in others ant Only 2- coord is positive
"
ts
2nd
•
3rd
#5
Only y-cond is
All lines are -'re
[«2» pass
= (sine formula."}}
SM
Jabc Cos A (cosine, fomula)
(a) alb cos C + c Cos B}
When any three parts of a triangle are given provides
that at least one of thes
[ { these is a side, the ai can be solved by any of the above relations Example 4. In 4 ABC "if £A=1051€ = 60°36=4
the triangle {
Solution
A+B+C=180.
B=180
=15
a
"from" sinc" formula, sin 105 from Sin 105
SIA 15
gɩ <s sum OT OF
4. I solve
**
Sin 15
SM60 45 105
Sia 15 #sin 75
No.
6.6021
STATE) T 9849
0.5870 Num.
SMIS Exp.
T.4130 11740
3
From
SM 60
SM IS
re = 4s 60
•No log
Sin 15.
Sin 60 Num.
0.5021 7:9375 0-5316
130
. Exp.
Livi
Hence, we findì.
Sine & COSRCANÉ:
+
'others are **vc.
and the.
"Cosine & Secant "Hangent # cotangent.
==
--
"All the fundamental formulae, such as
#
1
sinta + cos2 = ! ̧
1 + tan' = secxx, held in all cases, (ie. true for any Example 1 If tan A = -1 find Sin A + cos A
The boundary line of A, as shown, will lie either in the 3′′,
quadram
Solution
(OP) or in the 4th,
"gund cas op's
In either case, 'OP=OP":
From 2nd qued sin A==
cand OP Cos A· cond
quad Sue A
=*/7
+15
There are two corresponding values for both
cos A to Car A
If, however, it is known
quadrant the boundary like of A lies, sin
have each a single value
Sina
Notes on Start, whenever possible, by finding the
smallest angle which cannot be obtuse.
Solution
5
From the above definitions, we find that PM and Org change as P moves round the circle
Hance,
the
rations of the trigonometrical functions of the ongle 0. depend on the poschon of P. As these 19
Sin de
COSINE
Cos Poto
love t
SPA FZD
7
me
And TANGANI Your 90--
拿耀
(2) Calculate the angle opposite to the smaller
the given sides
which cannot be obtuse!
of
(3) As a check, greater side is always opposite
greater angle (and alse,
Converske
And
a triangle cannot have two obluse angles
The sides of a triangle are 22+3,
x2+ 2x, show that the greatest angle is 126.
Let of be the angle opposite to (X*+7x+3) By cosine formula
(2+3+3)=(x*+ 2X)2 + (2243)2°
(x2+3x+3)* − (x2+5X) = (2x+3)* −2(2*+21}{21+3} Comor (2x^^52+3)( x +3)=(24+3)[(2x+3)− 2 (X*+ 2x)(8X] (22/3)(x+1) (2+3) = (24+3) ((2x+1)=2(x*+2x) (050) 2x+3 is one side of the given triangle
2243 - 2 (x^422) ·Cos of
歡體
日三月一年七六九一层公年六十五國民華中
TELL
元文 旦教 聯團
【
(E)
波學校,於元年,樂, 高舉,在抗戰期間
上的良好 一,値得備魂之處蝻 午三時,在該校语堂]
K › REZENST 學,參加團灣貝生藏 沈亦珍博士致開會詞、鄒衍大、為京明姬 陈舞,然煜斯槍。 -EXED-KEEBIKER 【全橋出席學生族們找 半餘人,首由校長 公校,雞陸鍋,诚自强 系友會逸出,隨師傅 ,拋即開始遊燬,筐破十人、氣氛熱烈。 3 行 感愉快,北面板 校大禮堂擧行视 筱貞、蔡俊傑、莺新 賢博士主持抽獎,獎 ,總之,此次日食之,浙公學昨晚七時在試其析、嫣爲和、古瀬餐學,郭薇公 法培容耢生自覺良,氣氛館歡樂。服、古國文、梁嘉方 研習遊修大計,搭多 理秘俪化,是教育方 濟一堂,恭新年快 惡、朱淑、蔣醫時行樂,應定下一年 合唱,銀盤盤,灰諂致新年賀詞,多祝 機工程學校,戰前平
| 牛樂會,到師覺,瓷季維夫婦、朱區多由然發首長及各 (五)北角、郭金盛、施振苯、改謝同學、寧雲光 、李錫宗夫婦、黨楨防效。會長斑偉君亦 (6) WEP
IKERK
設置兩項助學金
一九六七年至六八年俁0衒於該大學, 六特凯 英國以式葱EXETFR 大學號宦佈-一九六七至 資格者可於本月底前提出申請 申請人須已具有博士學位 合 TKUS th
[千人、〔南师
工程學校晝生各有慶祝
一. 中英文校協會、珠海 、元培書院、浙公學 遠東中學、鄧鏡波學校 書院外文系、世界電橋底增新的包千餘,口季餘合奏,女生間聯歡宴會。
無綫電電訊及裝械工 博士學位者,享有優先權。 、晚 多數間闖入國,參、無變、灏育、心理、治洪、法律、政治制度、經濟學、社會 一、數學、物理、化學、化工、、地質、植物、物、工料 凡研究英文、法文、德文、西文,錢文、文、神學、哲
一番 月中旬日本及台灣現,同時在證貌和实用、馬頭頂等一在許始熱而散。(港校監麥詠習中、系主作密祧融的校友,“好轉。經過多
用
考察教育,已於去年務方面令人更爲饼服,每人薄禮包一份, 紙紹芳女士,會於上 先激育榮成的良好表,均來自京士柏及何,卻病而出,至九時而戰餐築會,強有整元且假期,該資佈, 年,這東中英文中謝校長過的數字都錄, 超深邊包之潼義。致潼南山龍水,碎花宇曲 總獲行新稱同學年爾德,滴逐一九六七年,訪問學人劉向基金會及大學交一館要觀,是 (特羅♪郡箕漚事上,學生却没有車道原築及繼主持分腳 文大學新雅書院國榮 流影院外文系群盹,返港就藥者,均於里動簡學入可以參加研院對貓會,並沸防橫圈之監國,阿以控 食演奏-湖春晚,時,假中用紅寶石酒 界工商業創立同基 用武級教齦之休息室。末還者並可由大學印給宿舍,學年終了時間
外
紅酒
系有年宕晚
主該
館
網酒八珠
元磯
返
#
一進復 額
堂,熱情詳俗,盛况
一番上問
THE QUEIN'S DRIVF. NORTHCOTE HOUSE.
EXLTER. UNITED KINGDOM.
UNIVERSITY OF EXETER. ACADEMID REGISTRAR.
元旦新年團拜,報導到遵守良好的社會跌,鮑斯高墨總院之首最會,元且日下午一時, ,特於昨農主焘該校, 從該育上, 已經遠 長榮乘邦、保安概及私立中英文學校協涖年 服務,各方面的學號,同機獲得美好的一時,做座大埔道七 、蘇生、余游 尹心、夏仲縈及全體 2010年大中型海中小學及幼猴圖殺 館目多引以姚兒常。年國弁。到有夜後雄 雪亭侯學、王華中、 也是我的移甘和柳、下、秘空前。「港 除夕搭國泰航接反捲,因擒日本的猴子,我引證品是由名聚會、《國際肚)泄九如泉的會長實中、 紅生間有相驗十餘年 〔港香港元 迅中、磁能啞夫婦慧芳、晶、蔡澄 KLERPRES. 2C EEGIF! NXR CSKHKOFT 9-ALAKTEER-KENE-OBCHE 甜甜、周松-系幹事總 任資公恩博士、及外 酒花猴,筵開歡,月卅一日前提交談大學,地能如下: 大剂,黃遠東大類, 商務余蒸廉、麵 倘有教育
三好,尤其學生對社會與協等效材不少· 月 學年幼稚教育澹步良 實的資料和電化教學(天
1與東京年
真
第在育
轉厚位威 【扃嫁材究程瞪,年始在卅以了,志在研究
【金,以兩年假期,但亦可延至三年。魏學金之給與日期,一 -HA-RUBELFOR-TEIN · ZFS KE-HENTKAKEKME-EEILEIBNI• G
交通上能遵守秩序! 問學校,其中有三十六年元月櫛破、孫東妈、羅雅、共數百人。首由校
1間私立小學教育水準,茶盤,到有教授灣區 黃定遠、愛期、李立林中及系主任周公
COKE-BEU SY · SERET TEBREK - RUE EXELP FARK.BREY KOBY
A
七年二月十七日前送,地址同上, 申請書暨附酎作目錄及两位介紹人名住址,並於一
14
(WHY?)
Exp
cosa is negative, the boundary of of lies either
the 2nd or the 3" quadrant.
∞ = 180 ± 60° je. 120′′ or 240
But & is an im, a of a at hence × 4240 ̧.°,000/80
e. The greatest int. < is 120°
xample & Two angles of a triangular freid
Solution
and 45°, and the length of the side opposite
the latter is one furtony, find the area.
ABC denote the fangakt field.
B=45°
In Example 6, we can find the area directly
by the
ula
HINTS
& ANS. To fr 9
Exp = {Six 60 ){ cms 3 0) { Cat 45)
= (£) (+) (1)
ANS
=(Sec 60){ sú do + Cos 30) ( Sih 60 - cos 60)
= SEC 60 ( sin do + cassa) ( Cos so - <30)
sec 60, (cos*go — sin*30)
Each int < Each ext.
=
22
184
170
70* — 7087 rad. — 70 rad The length = 44 of 276.
4, Proof: [sino + sin(1-0)] + [:cos &~
= ( sih * + cos 8)*+ ( cos ✪ -
ANK ST, I
ANS. 33.ft.
sin #32
5 From Example 5. Radion measure of on anole ·
~ Subtending arc
Example 2) Find the raluc
(a) { 4 ces o°`sin* 270′′ – 3 cos 180° tan 45° |
CO 470 P
Fun 70
6=1 furlong =220 yd.
45
NO TION
tive i positive f› increasing in absolute value ~'ve negative,
decreasing in absolute value.
B
Hom «, Sum of A,
= 180 − ( 22445)
By Sine formula.
SMA
Sin B
C Sin C
3h 45
SIR 22+
420 yd Sin 45
a
SM 112€
220 sin 227
SM 45
SIA (122
220 342,
Siλ 45
377
+
5 Lan TT cos 21+ Sec 21 - 2 cdo 37
Jolution: (a) Exp.=4(1)(~1~senco,
(b). Exp
0+11+2
The follwing is a summary of the results" established: Sin (90° ± 9°} == + cos 8° Forca) SM(F±or) m + cas de
Sin (180° ± 8°) = + Sin O'
± sino
cos (96 +8)=7 Si D cos (180 + 0") == COSA Cos (360£0") == + cos п
Tan (90±6) = + coto tan (180°10′) = ± tan o tan (3607 0) — 7 tan &
Sin (360 ± 8°)
5/ (7 200) —
Six (2# 2×) = ± SÜα
+
=F SÍMA
=-Cas &
Cos(272×) = + Cosa {(2) tan(‡tα) = & coα
1
tân (1±os = ±. Lanc (în (272×)= * tan¤
Example. 3. As shown in fig., PQ=QR", prove that
cot
tp: == ( cot∞ + catlys.. "Proot From da OPN: cat o = ON
"Adding,
From the ORN1 cot &-
PN.
2N
In cot of + cat i on ON
By the area formula,
Area of the field = ± ac su
220 SM 227 ) ( 220 304 11/23
110 x 230 x Sin 24‡× SM ÉTÉ
Sin 45
11210038 yo
NOTES Us If the additional relation "Så 45=2 sin coste
ứa girin, then the exp becomes HO XITO {(2) In general, if we substitute the sine formula into this area formula then we find
Area co➡tac Sin B1
-+(£3MA)(SMC) SM B).
.",
SMASMC)
SM (ATC)
***
7.5.ft.
2.5 ул.
120* *-
{ ANS. 15 57.396"
1 or
The angle
Exercise 10
1 Find the value of、
(a) 3 sm 0° sec 186" + 2 Csc 90° - cos 360°)
#
(b) a sec* m. cos. 0 + 3 sm2 21- CJC I
2, As shown in fig, AD is a median of AABC" use the
fact, proved in Example 3.
cot
kg
#o
Empressi
in terms of 8 Cand evaluate
& in the following cases · Cillustratig
each by a rough figure);
(a) 8=35% caso", do B35 C=105", «C, B=50°, c=35*
triangle are FE-12 and
By Two sides of a
and the included angle is 60°, solve the triangle: and find the area of the triangle,
1
Q* + b2) C2 + a* + ab +
"=0, where a, b, c are the length of sides of DABC, prove the C
تار
or 120",
5. The angles of elevatim of the top k of a vertical " mast from two points A, B on the same level as its foot H, are 32°14′ and 22°28′ resp, If the height of the mast is geft) and the bearings of A and E from H am 270° and 200° resp., find the distance AB, and the “ bearing of 8 from A3
Page 20Page 21
No comments yet.
Private notes are available after approval.