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trigonometric functions

trigonometric functions. Dedicate: To our teachers who have always taken care of us and supported us: we offer this little work and we hope you will like it. With all our love and respect to you. Introduction .

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trigonometric functions

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  1. trigonometric functions

  2. Dedicate:To our teachers who have always taken care of us and supported us: we offer this little work and we hope you will like it.With all our love and respect to you.

  3. Introduction Mathematics is a very important subject that has many different uses in the natural world. It improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. Now it's true that triangles are one of the simplest geometrical figures, yet they have varied applications.

  4. Introduction In this research we will first define trigonometric functions, then we will know their importance in the study of triangles in practical life, especially in the study of elevation and depression angle which have many uses in finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps).

  5. What are trigonometric functions? In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

  6. Problem 1 Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30o and 60o respectively. If the height of the building is known to be h =100 m, find the distance (in meters) between the two men.

  7. Solve the problem And  Tan B = tan 60o = h / BC =100 /tan60Now the distance between the men is AB (x)  = AC − BC = (100 /tan 30) − (100 /tan60) = (173.2) – (57.7) = 115.5 m Givens: h =100 m Angle A =30 Angle B =60 In the figure, A and B represent the two men and CD the tall building. Tan A = tan 30o = h / AC = 100 /tan 30

  8. Airplane 2 miles Ø Airport Ø Hyp Opp 5 miles Adj Problem 2 An airplane is flying at a height of 2 miles above theund. The stance along the ground from the airplane to the airport is 5 miles. What is the angle of depression from the airplane to the airport?

  9. Solve the problem Given: Height = 2 miles The distance along the ground from the airplane to the airport = 5 miles Solution: Tan Ø = opp / Adj Tan Ø = 2/5 So Ø = 21.

  10. Conclusion To sum up we can say that math makes us smart and adept at solving tricky situations. It’s true that trigonometric functions have many applications in our daily life. Calculating elevation and depression angles, heights and distance are all examples of the trigonometric functions applications. Knowing elevation and depression angles, heights and distance is so important in engineering and aviation. Finally, we would like to say that we were very interested to know about Trigonometry applications in our daily life and we found them so useful and very important. At last but not least, we would like to thank every one who helped us and we hope you will find our research useful …

  11. Done by: Ekhlas Abdullah Moza Al-mahmoud Noor Muslim Class: 12/3 Teachers: tahani Abdullrahman

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