1968-12-31 — Page 24

掌四第張六第

日二十月一十年申戊歷夏

WAH KIU YAT PO

鬆日橋華二期星

19605959 FUR

1969

SAY?

數學科(九)

歐陽鋊文

英文科(九)

桂枝

MATHEMATICS (9)

LESSON 9 RADIAN MEASURE

ENGLISH (9)

then,

circle cemre o, as shown,

are AB — the radius c

«AOB = Constant-

circles

rs in me given figure BO to meet me of at. c.

BIL BA

art BAC

This

Suppo

·BOA

onstant oted by hate

angle

Then

180°

of 2

Constant

called a radion; onet;

of 366=1*

Which is the termula connecting the sexagesimal measure ( in digras) and the circular measuk

fadians) of an angle

In general,

Then we have

NOTE

* = the magnitude of the « in deg. Ôm the mag of the same « in nadiam

DIAN). A radian is an angle subtended of the centre of any circle by an are equal in length to the radius of the circle.

Since a radun is a constant, it is taken as a standard unit and the number of radians contamed any angle is spoken of as its circular (radies) measure In this system, an angle is usually

a “mere number, the unit being

denoted

implied.

NOTE 2: The symbol is always denotes a no., 5.14157-

When the symbol stands alone, without ref erence to any angle, it denotes 3.141592 shen symbol π is used to denote an angle it is again

3.141592 -- (the number

Then

radians

radian measure

of radians in 4°11′33

1951=1,120

180.

Example 2' Convert 71⁄2 radians to sexagesimal measure.

Precies

Answers to Paper

Nowadays people are too absorbed in their work to find out the causes of things, Perhaps we can account for this. Han has been advancing so much 80: that he does not have to worry about the nature of things. All he worries about is to achieve things quickly. But is it right to do so? It seems that, doing so, the standard of social conduct and the Improvement of the mind has been degraded and peo lack constructive leaders to guide them.

Paper I

日一册月二十年八六九一公年七十五國民華中,真教焦费

Unless you are used vu it, an April morning is not. the best time for plunging into cold flowing water. Anthony, sitting on the edge of his bed, with a hand absently fondling the ears of Cerberus, was wonderi whether, in his answer to Mr. Fordages letter, he should point out that, though a morning bath waa referred to as something customary, his habit was to bathe in warm water once a week, on Saturday nights. However, he didn't want to start his life at Easter. How with disobedience, so he pulled off his warm nightshirt, put on a machintosh that made him shiver, and ran out to the head of the steps. He called to Cerberus, who opened one eye, gave him a knowing wink, am got his head down again between his paws.

Ine stone stairway was wet with dew, and cold. Anthony's naked toes curled and he stepped gingerly But the sun was shining upon the daffodils, and the backbirds and thrushes were full-throated in the hawthorn hedge. It was half past seven. The bleat of lambs came from the surround fields, and too nigh to be seen, larks were in the sky from which the sun had not yet burned the last mists of the night.

anthony stood still, listening, and he could hear the clear voice of the water, a silvery constant thread on which all the other sounds of the day were hanging. Sundenly, he was hearing nothing in particular, but everything was one thing, himself

part of it: the strengthening sunlight, and the ILovers and the birdsong, and the deep troubled voices of the ewas answering the quavering, lambs, and the ripple of the stream, and Valpy snorting in the barn: and he ran down the stairs and across the lawn and along the edge of the water, his toes rejoicing now in the clear diamond wetness of the grass am his eyes in the. golden blobs of water-buttercups cups indeed, full to the brim with dew, And here were the alders. enclosing what Mr. Pardage called his Parson's Pleasure, where the stream deepended to a pool, and hazels were among the alders, dropping from their boughs golde dusted catkins, drying in the sunlight like the tails of new-dropped lambs.

He threw off his mckintosh and daved, an ELIS

fingers were at once among the pebbly nuggets that made the stream-bed an eldorado. He came up with a handful, gasping, for the water was as cold as though it were the sweat of a glacier, and he stood, dripping and shivering, while Cerberus, who had at last decided to follow, stood by, his read tongue protruding, laughing in derision, as if he realised, what only now occurred to Anthony, that he had come without a towel, well, that was something to remember next time? the boy thought, wringing water from his hair, and this first time was something to remember, too, He pur on his mackintosh, went back to his room, and towelled himself till he glowed. Never, he thought, have I till now started a day like this; and the memory came to him of the rush downstairs in Megson Street, and the rush through breakfast with uncia Korace coughing from}

some imagined catarrn, or Wraming. From some imaginea lumbago; and then the rush to school, and the school- bell ringing, and the calling of the register,

unoose the correct answer:

Mr. Pordage a letter told Anthony

1. not to plunge into cold flowing water.

2. not to plunge into cold flowing unless he was)

used to it..

3. to barne-in ward water once a week. 4. to bathe in warm water only an Saturday: 5. to bathë every morning,

Anthony bathed in that part or the river.

1. where the stream had deepened to a DoDlat

2. where the stream rippled.

3. where the alders grew.

4 where the hazels grav;

5. where the water-buttercups grew,

Anthony thought that the next time be bazned)

he ought

1, not to bring his mackintosh.

2. to bring his mackintosh

3, to bring a towel.

4. not to bring a towel,

5. to be more careful

In this piece, Cerberus vas

1. Anthony's friend. 2. Anthony's sister,

3. Anthony's brother.

4. Anthony's pet. 5. Anthonyls companas

Uncle norace was

1. a hysterical persoEL

2. a critical person.

3. an imaginative person

4a sensitive person.

a person who frequently suffered from attacks. of rheumatismi -

II. Give för each of the following words another

expression of similar meaning to that found in zam passage.

1. plunging

2. fondling

mowing troubled eldorado

by sweat.

7. protruding 8. derision.

9. glowed

10, gingerly

SOL

Then,

in degree

316 (in)

face is 20°

(at noon)

Example 3: Find the numerical value

Ex

(a)

(b) (Cos 7+ sin Z ){ cas

= Sin (186) cos(1) cat (120°)

-(4)(4)(1)

के

Exp

( Cas 30.

Sin 30°)( Ces 50%

Sin 60°) Secto

( Cos I + sin + ) ( Cos + = $in 5) sec #

NOTE: From the abol

problem, we find

Radian of an angle = subtending arc

Example 6. Two angles are such that their dif

and their

in degrees.

is to radiams; find the angles

ALB be the two such that

And From

Cos 30+ smsa') (Sín 30° = cos 30") se€ 60°

CA: 30°)(520 60°)

As shown

the

of lighthouse- positions

the

In of AABE <LAB=90-32 — 58′′

KALB=5145

AB=10313M-

LAW AB· Cos LAB

it ca 58 - 7A5

Lit P. & be the two positions of the

observer.

<APB=70", LARIS = 143" 24

PQ = 630 medes

From APQ

AP = PQ cat PAQ

AR

Let ABC

AB = AC

=630. col (1/43°29-933

630 cot

~467.8.m.

Example

În running a race

Exam

n uniform speed on

Circular course a man in each mbuk han- verses, an arc of "circle ishich subtenda: 2 & radians the centre of the course.

each lap is 792 ya, how long does be

(like # #

take

"run

Oce of the circle =792 ya

293-3d, taking T=2

126 ya

the length of are traversent in

Hence, the mam

HINTS

Prodiera QA

vertex

meet the sphere again at Cushich is the highest pt. of the splore) If the sphere touches the cone at B Then

ABC JAC

70.5714

5714

de at the cerke +1.95, Find the radius of,

the ver

balls.

arc of 17 yd 143#

circle an angle

the circle in inches

be the radius of the "circle

of the same circic the length of the arc

And the

gd 1 H. 34 =524H.]

No. $2.15-

Adding,

70774

Num.

#7973

and let BC

6x units, the AB=13x unis Drop AN LBC then GN=BC œ 32 unit From A OBAN:

26AC

Find the value

Express

in radians, the extens and interior an

a regular polygon which has in sides.

angle at the centre of a circle whose radius 2.5 yd. is subtended by an arc of thas Hi the angle, in degies 3 in radians. *

4) show that the sum of the specam

caso

angle

Contains * soxagesimal minutes

& radians Find

state the multiplier necessary conver into sexagesimal minutes