TRIGON

FUNCTION

Al-Wakra Secondary Independent Girls SchoolScience

department

Name : Alaa Jalal & Somaia Fadile & Riham Sobhy Grade : 12Class : 1Subject : MathTitle: : TrigonSupervisor : Miss. Sabah RajabThe date of submission : 5-5-2010

Contents

topic page

Introduction 3

Angles of elevation and depression …

Question (1)4

Question (2) 5

Two of the most important forms of

trigonometry & measurement 6

Use program (Wolfram Demonstrations

project)7

Conclusion 8

References 9

1

certain people in the world are

special ,kind and giving

they bring sunshine and

happiness to the

lives of others in times of need

and they spread joy

and smiles wherever they go

my teacher is truly

someone special

thank you

is the right word

for right deed done.

2

Dedication

IntroductionTRIGONOMETRIC FUNCTIONS ARE OFTEN OMITTED IN BASIC CALCULUS COURSES FOR STUDENTS NOT MAJORING IN THE

MATHEMATICAL SCIENCES. HOWEVER, THE SINE AND COSINE FUNCTIONS ARE EXTREMELY USEFUL IN MODELING CYCLICAL

TRENDS, SUCH AS THE SEASONAL VARIATION OF DEMAND FOR CERTAIN ITEMS, OR THE CYCLICAL NATURE OF RECESSION AND PROSPERITY. THE FOUR SECTIONS WE PRESENT HERE ARE

DESIGNED WITH THIS IN MIND; WE ARE CONCERNED LESS WITH THE GEOMETRY OF TRIANGLES THAN ON APPLICATIONS OF THE TRIGONOMETRIC FUNCTIONS IN MODELING REAL LIFE

SITUATIONS.

and the definitions of the trigonometric functions give rise to the following fundamental identities:

3

** Angles of elevation and depression **

1. An observer in a blimp sights a football stadium at an angle of

depression of 34 . The blimp’s altitude is 1600 ft. what is the horizontal distance

from the blimp to the stadium? Round to the nearest foot.

90 – 34 = 56

Cos Ѳ = a / h

Cos 56 = 1600 / h

1600 / Cos 56 = Cos 56 (h) / Cos 56

1600 / Cos 56 = 2861.26

1600 ft

34

4

tan Ѳ = o / a

Tan 78 = o / 6

O = tan 78 ×6 = 28.22

2. When the angle of elevation of the sun is 68 , a building casts a shadow

that is 6 m long. What is the height of the building to the nearest tenth of a

meter ?

78

6 m5

Two of the most important forms of

trigonometry

The measurement

Sin Ѳ = Opp / Hyp

Cos Ѳ = Adj / Hyp

6

7

Use program ( Wolfram

Demonstrations project )

Conclusion

8

BEFORE I WRITE ABOUT TRIGONOMETRY, I WOULD LIKE TO EXPLAIN ABOUT THE MEASUREMENT OF ANGLES , A CIRCLE COMPOSED OF 360 & 90 & 180 & 270 DEGREES, AND THE SPECIAL ANGLES ARE 30 , 45, 60 AND 90 . THE TRIGONOMETRY AS SEEN IN THE PREVIOUS THERE ARE SIX TRIGONOMETRIC FUNCTIONS. THE TWO MOST IMPORTANT ONES ARE SINE AND COSINE. THE OTHERS CAN BE DERIVED FROM THESE TWO FUNCTIONS. THE TRIGONOMETRIC FUNCTIONS ARE BASED ON THE RATIOS BETWEEN SIDES THAT EXIST IN RIGHT TRIANGLES.THESE OPERATIONS BENEFIT US IN OUR DAILY LIVES AND USED IN SEVERAL AREAS SUCH AS BUILDING A HOUSE OR TO KNOW A CERTAIN DISTANCE, ETC.

… In the end, thank everyone who helped me, and I wish that the research will be useful for all and I apologize for all the shortening, Suffice it that I did not spare any effort in trying to reach the degree of perfection, but only God is perfect. I wish always for your sincere affection and appreciation and ask God to help and guide.

References

9

1. http://www.sosmath.com/trig/Trig2/trig2/trig2.html

2. http://www.clarku.edu/~djoyce/trig/functions.html

2. Schaum's Outline of Trigonometry Paperback

Author), Robert E. Moyer ) Author) "A degree)

1. Mathematics HL for inter national student , page 569 , chapter 8 , Angles of elevation and depression , 4 – 8 (1-2)

3. http://mathsisinteresting.blogspot.com/2008/08/negative-angles-used-in-trigonometric.html