Introduction to Trigonometic Ratios

Learning Objectives
1 understand cosine, sine and tangent of acute angles
2 apply trigonometric ratios on simple problems

Title page story, oral and dictation
There is a frog staying at the base of a cylindrical well with the depth of 10 m and base radius of 2 m. Every night, the frog looks at the moon at the centre of the well. Without taking the height of the frog into account and assume it will not climb up the well, at where, the centre or edge of the base, can the frog obtain a
larger angle of view 0?(theta)

also theta, alpha, beta, phi

Hints
1 Draw the possible angles of view of the frog when it is at the centre and at the edge of the base of the well.
2 At where, the centre or edge of the base, can the frog see more? Explain briefly.

Preview
abbreviation, corresponding
Pythagoras' theorem

11.1 Cosine Ratio of an Angle, Origin of trigonometry
11.2 Sine Ratio of an Angle
11.3 Tangent Ratio of an Angle
11.4 Applications of Trigonometric Ratios
11.5 Properties of Trigonometric Ratios

11.1 Cosine Ratio of an Angle
Mr. Lam is planning to put up a ribbon of coloured flags from the ground toen the top floor of the school building. It is known that the angle made by the ribbon with
the ground is 25, and the ribbon attached to the ground is 32 m away from the school
building. Can you estimate the length of the ribbon?

A Meaning of cosine
hypotenuse, opposite side, adjacent side
**cosine ratio: adjacent side/hypotenuse
Finding cosine ratio with the sides given
Finding the adjacent side with the cosine ratio given
Finding the hypotenuse with the cosine ratio given

B Origin of trigonometry
trigonometric ratios
trigonometry meanings surveying and triangle
architecture, surveying, engineering and sailing.

level 2
1 horizontal distance travelled by the car
2 the distance between the foot of the ladder and the bottom of the wall
3 the kite and the length of the string
4 diagonal and the dimensions of the field

C Use of calculators
CASIO fx-3650p/fx-3950p

D Finding angles through cosine ratios

**Chapter Summary
Hypotenuse, Opposite side, Adjacent side

Additional Questions
2 Mr. Chan lives in a 3-storey house. At a distance of 1.5 m from the house, there is a lamp post. During a windstorm yesterday, the lamp post fell and leaned against
his house with its top locating above the roof. at noon, the lamp post casts a
shadow of 0.5 m long on the roof. Mr. Chan is going to claim the damage from an
insurance company. Can you help him solve the following problems for his insurance
claim?

Repeat and check carefully again

Spelling

Opening with
*mess
message messenger

*pass
passage passed

*re
require repeat remind reorder

*ten
tendency tense

Ending with
*age
passage message

*cy
tendency policy Lucy

*ire
require sire fire hire

Measures of Central Tendency

Chapter 13 Measures of Central Tendency

Learning Objectives
1 find the mean, median and mode of a set of ungroup data.
2 find the mean, median and modal class of a set of grouped data.

Title page story, oral and dictation
In a class od 39 students, the average weight is 39 kg. After a new student has joined the class, the average weight becomes 40 kg. What is the weight of this new student?

Hints
1 What is the total weight of the 39 students? 39 x 39kg 1521kg
2 After the addition of the new student, what is the total weight of the 40 students?
40 x 40kg 1600kg
3 Find the weight of the new student. 1600 - 1521 79kg

Preview
Basic technique

13.1 What is Central Tendency?
13.2 Means
13.3 Medians
13.4 Modes and Modal Classes
The mode of a set od data is the item with the highest frequency.

**Chapter Summary
1 Mean: Sum of all the data, number of data
2 Median
a For a set of n data arranged in ascending or decending order, if n is an odd
number, the median is the middle term, if n is an even number, the median is the mean of the two middle terms.
3 Mode and modal class

Additional Question
1 The following table shows the number of words in three passages, and the time
required for Sally to finish typing them up.
2 Choose a question you are interested in and conduct a statistical survey on it.
eg the number of late arrivals and absences in your class last month.

Repeat and check carefully again
Chung Tai Educational Press
New Trend Mathematics S2B

9 Algebraic Fractions and Formulae

1 master the operations of algebraic fractions.
2 know some common formulae and substitute values into formulae.
3 perform change of subject of a formula.

有心學？還是有心懶？

很多新進的員工都說，很想學多一點醫療知識和技巧。起初，我滿心歡喜盡心盡力的教導。但我發覺，教的時候她們都似乎很認真學習，可是到臨床操作的時候，卻總是一塌糊塗。

我滿腹狐疑的請教高人……「她們學習的時候，有沒有做筆記呢？」「沒有啊！」「咦？中醫學問艱澀深奧，不記錄下來，又怎會記得呢？」「噢！」「她們發問的頻率如何？」「甚少！」「告訴你，她們不是有心學習的。」「啊？……真的嗎？」「你不妨設立評考制度，觀察一下她們的反應！」

得高人指點，馬上加設考核制度，結果雞飛狗走，唔再學了。原來她們並非真的有上進心，只不過……學嘢當然比做嘢好，既有工資，又有嘢學，學不成又無責任。

高人說：「有心學，從你與病人診症、施針、處方開藥的時候，只要細心聆聽、觀察、反覆研究，將讀書時學到的理論跟臨床實踐結合，便能加速融會貫通， 成為自己的學問……這才是真正有心學習的人。」

一言驚醒，難怪現時的學生哥，讀完又讀，中學畢業，考不上大學的便讀個副學士，有幸考上大學的，讀完學士又想話再深造，原來只是逃避，不欲投身職場吧！

有心學？還是有心懶？有分別的。

下學期的新任務15/2

Chapter 8 Inequalities

1 understand the meanings of ineauality signs.
2 explore the foundamental properties and some laws of equalities.
3 solve simple linear ineaualities in one unknown and represent the solution on a number line.