Trigon function

1. Al-Wakra Secondary Independent Girls School Science department Trigon function Name :Alaa Jalal& SomaiaFadile & RihamSobhy Grade : 12 Class :1 Subject : Math Title: :Trigon Supervisor : Miss. Sabah Rajab The date of submission : 5-5-2010

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3. Dedication 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

4. Introduction Trigonometric 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

5. ** 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 34 1600 ft 4

6. 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 ? tan Ѳ = o / a Tan 78 = o / 6 O = tan 78 ×6 = 28.22 78 6 m 5

7. Two of the most important forms of trigonometry Sin Ѳ = Opp / Hyp Cos Ѳ = Adj / Hyp The measurement 6

8. Use program ( Wolfram Demonstrations project ) 7

9. Conclusion 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. 8

10. References 1. http://www.sosmath.com/trig/Trig2/trig2/trig2.html 2. http://www.clarku.edu/~djoyce/trig/functions.html 3. http://mathsisinteresting.blogspot.com/2008/08/ negative-angles-used-in-trigonometric.html 1. Mathematics HL for inter national student , page 569 , chapter 8 , Angles of elevation and depression , 4 – 8 (1-2) 2. Schaum's Outline of Trigonometry Paperback Author), Robert E. Moyer )Author) "A degree) 9