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TRIGONOMETRY IN EASY WAY
Today is the time of Scientific Discoveries in which in Science field, technology
field and so many others
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The fundamental trigonometric functions
like sine and cosine are used to describe the sound and light waves
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Trigonometry, the branch of mathematics concerned with specific functions of
angles and their application to calculations
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The field emerged in the Hellenistic world during the 3rd
century BC from applications of geometry to astronomical studies
Trigonometry is a study of the relationship of angles, lengths, and heights
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Now it has spread its application into wider fields like
engineering, physics, surveyors, architects, astronauts and even in the
investigation of a crime scene
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C
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Hipparchus also developed the first accurate star
map
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Hipparchus was the first to tabulate the corresponding values of arc and chord for
a series of angles
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You may find it helpful to remember
Sine, Cosine and Tangent as SOH CAH TOA
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Mainly there are three functions use in trigonometry
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Sine (Sin)
2
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Tangent (tan)
And the other three functions are derived or based from above three functions
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Cotangent (Cot)
2
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Cosecant (Cosec)
Trigonometric identities are used in our real life like finding the sine of an angle
will help when determining how much of a certain material is needed to use in
order to construct the building
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Trigonometry plays a major role play in our business industry, where it allows
manufacturers to create everything from automobiles to zigzag scissors
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Trigonometry is used to in measuring the height of a building or a mountain
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Euclid (who lived around 300 BC) made heavy use of chords of circles, which are
completely equivalent to sines of angles
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The first person whose name we
know who worked with sines was Aryabhata, who lived around AD 500
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In Electrical Engineering, Calculus
(Integration) is used to determine the exact length of power cable needed to
connect two substations, which are miles away from each other
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People can use panels in rooms such as studios and turn them in different
angles so that the music waves bounce off just right to make the song sound
smooth and even
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For any right triangle, there are six trig ratios: Sine (sin), cosine (cos), tangent
(tan), cosecant (csc), secant (sec), and cotangent (cot)
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Trigonometry can be simply defined as calculations with triangles involved with
the study of lengths, heights, and angles
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For instance, it is used in geography to
measure the distance between landmarks, in astronomy to measure the distance
of nearby stars and also in the satellite navigation system
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For example, trigonometry is used in developing computer music: as
you are familiar that sound travels in the form of waves and this wave pattern
through a sine or cosine function for developing computer music
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Example:
The distance from where the building is observed is 90ft from its base and the
angle of elevation to the top of the building is 35°
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Solution:
Given:
1
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2
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To solve and find the height of the tower by recalling the trigonometric formulas
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So, using the formula
of tan
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4738
h=42
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64feet
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It has taken into account the speed, direction, and distance as well as have
to consider the speed and direction of the wind
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This equation cab is solved by using
trigonometry
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This calculation will
be solved using the trigonometry and find the third side of the triangle that will
lead the aircraft in the right direction
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The functions of
trigonometry are helpful to calculate a trajectory of a projectile and to estimate
the causes of a collision in a car accident
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Trigonometry is often used by marine biologists for measurements to figure out
the depth of sunlight that affects algae to photosynthesis
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Trigonometry is used in navigating directions; it estimates in what direction to
place the compass to get a straight direction
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***For your Knowledge***
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The calculus is based on trigonometry and algebra
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Trigonometry is used in oceanography to calculate heights of waves and
tides in oceans
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When you complete an undergraduate math degree, jobs like the following
become possibilities for you:
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Cryptographer
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Economist
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Financial planner
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Statistician
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Prepared By: Raja Jawed Riaz



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