how trigonometric functions are used in real life? -in chemistry trigonometry is used to calculate...
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How Trigonometric functions are used
in real life?By: Tahura Ashraf & Saraban Mem
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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.
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What are the trigonometric functions?
In a right triangle there are three major trigonometric functions.
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Special triangles;
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Trigonometric Functions
SOH CAH TOA1. SINE= OPPOSITE/HYPOTENUSE2. COSINE=ADJACENT/HYPOTENUSE3. TANGENT=OPPOSITE/ADJACENT
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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)
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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
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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
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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
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Trigonometry and Navigation:
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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.
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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.
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