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 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.

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).

 

Introduction

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.

Problem 1Two 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 .

Solve the problemGivens : 

h =100 mAngle A =30Angle 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

 

And 

Tan B = tan 60o = h / BC=100/ tan60

Now the distance between the men is AB (x)

= AC − BC( =100/ tan 30( − )100 / 60tan )

( =173.2( – )57.7) =115.5 m

Problem 2An 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?

Airport

Airplane

5 miles

2 miles

ØOpp

Adj

Hyp

Ø

Solve the problemGiven:

 Height = 2 milesThe distance along the ground from the airplane to the airport = 5 miles Solution:

 Tan Ø = opp / Adj 

Tan Ø = 2/5 So Ø = 21.

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…

Done by:Ekhlas Abdullah

Moza Al-mahmoud

Noor MuslimClass: 12/3Teachers:

tahani Abdullrahman