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Trigonometry is a very important tool for engineers. This reading mentions just a few of the many applications that involve trigonometry to solve engineering problems.

Trigonometry means the study of the triangle. Most often, it refers to finding angles of a triangle when the lengths of the sides are known, or finding the lengths of two sides when the angles and one of the side lengths are known.

As you complete this reading, be sure to pay special attention to the variety of areas in which engineers utilize trigonometry to develop the solutions to problems. Rest assured that there are an untold number of applications of trigonometry in engineering. This reading only introduces you to a few. You will learn many more as you progress through your engineering studies.

Virtually all engineers use trigonometry in their work on a regular basis. Things like the generation of electrical current or a computer use angles in ways that are difficult to see directly, but that rely on the fundamental rules of trigonometry to work properly. Any time angles appear in a problem, the use of trigonometry usually will not be far behind.

An excellent working knowledge of trigonometry is essential for practicing engineers. Many problems can be easily solved by applying the fundamental definitions of trigonometric functions. Figure 1 depicts a right triangle for which we will express the various trigonometric functions and relationships that are important to engineers.

Triangle for definition of trigonometric functions.

Some of the most widely used trigonometric functions follow

sin ( θ ) = opposite side hypotenuse = B C size 12{"sin" \( θ \) = { { ital "opposite"` ital "side"} over { ital "hypotenuse"} } = { {B} over {C} } } {}
cos ( θ ) = adjacent side hypotenuse = A C size 12{"cos" \( θ \) = { { ital "adjacent"` ital "side"} over { ital "hypotenuse"} } = { {A} over {C} } } {}
tan ( θ ) = opposite side adjacent side = B A size 12{"tan" \( θ \) = { { ital "opposite"` ital "side"} over { ital "adjacent"` ital "side"} } = { {B} over {A} } } {}

The Pythagorean Theorem often plays a key role in applications involving trigonometry in engineering. It states that the square of the hypotenuse is equal to the sum of the squares of the adjacent side and of the opposite side. This theorem can be stated mathematically by means of the equation that follows. Here we make use of the symbols (A, B, and C) that designate associated lengths.

A 2 + B 2 = C 2 size 12{A rSup { size 8{2} } +B rSup { size 8{2} } =C rSup { size 8{2} } } {}

In the remainder of this module, we will make use of these formulas in addressing various applications.

Flight path of an aircraft

The following is representative of the type of problem one is likely to encounter in the introductory Physics course as well as in courses in Mechanical Engineering. This represents an example of how trigonometry can be applied to determine the motion of an aircraft.

Assume that an airplane climbs at a constant angle of 3 0 from its departure point situated at sea level. It continues to climb at this angle until it reaches its cruise altitude. Suppose that its cruise altitude is 31,680 ft above sea level.

With the information stated above, we may sketch an illustration of the situation

Depiction of aircraft motion.

Question 1: What is the distance traveled by the plane from its departure point to its cruise altitude?

The distance traveled by the plane is equal to the length of the hypotenuse of the right triangle depicted in Figure 2. Let us denote the distance measured in feet that the plane travels by the symbol C . We may apply the definition of the sine function to enable us to solve for the symbol C as follows.

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution

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Source:  OpenStax, Math 1508 (laboratory) engineering applications of precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11337/1.3
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