How Trigonometric functions are used

in real life?By: Tahura Ashraf & Saraban Mem

What is trigonometry?

It is a portion of mathematics which deals with the relationships between the sides and the angles of triangles and the calculations based on them,especially trigonometric functions.

-The word trigonometry is originally a Greek word translating the term “trigonon” as triangle and “metron” as measure.

What are the trigonometric functions?

In a right triangle there are three major trigonometric functions.

Special triangles;

Trigonometric Functions

SOH CAH TOA1. SINE= OPPOSITE/HYPOTENUSE2. COSINE=ADJACENT/HYPOTENUSE3. TANGENT=OPPOSITE/ADJACENT

Inverse Trigonometric Functions*Flip and keep the sign*

1.COSECANT= HYPOTENUSE/OPPOSITE (inverse of sine)

2.SECANT= HYPOTENUSE/ADJACENT (inverse of cosine)

2. COTANGENT= ADJACENT/OPPOSITE (inverse of tangent)

Trigonometry and its application in real life1.Finding height (buildings or mountains)

2. Navigation

3.Oceanography

4.Sound and light waves

5.Architecture

6. Video games

7. Construction

8. Flight engineering

Examples of Problems:A person 100 meters from the base of a tree, observes that the angle between the ground and the top of the tree is 18 degrees. Estimate the height h of the tree to the nearest tenth of a meter.

angle:18

100 meters

h

Solution: Use tangent : opposite/ adjacentTan (18 degrees)= h/100You solve for hh= 100 tan (18 degrees) =32.5 meters

At 57” from the base of a building you need to look up at 55 degrees to see the top of the building . What is the height of the building?

Answer :

Tan (55 degrees) = height/57

Height =57 *tan (55 degrees)= 81.4” 55 degrees

57

Trigonometry and Navigation:

How Trigonometry is related to specific subjects;Trigonometry is also used in engineering,chemistry, physics,and astronomy.

-Engineers use trigonometry to find angles, calculate torque values,and forces on objects.

-In chemistry trigonometry is used to calculate the distance and angle between molecules.

-In physics, trigonometry is used in rotational motion,gravitation, motion in a plane,wave mechanics,optics,electric charges and many more.

-Astronomers use trigonometry to find distance between stars and other objects in space.

-In criminology trigonometry can help calculate a projectile’s trajectory to estimate what might have caused a collision in a car accident or how they fell.

Work Cited:Ferrao, Livia. “Real Life Applications of Trigonometry.” Embibe Exams, 29 June 2017, www.embibe.com/exams/real-life-applications-of-trigonometry/.

Joyce, David E. “History of Trigonometry Outline.” History of Trigonometry Outline, mathcs.clarku.edu/~djoyce/ma105/trighist.html.

Images from google