Surveyors. That's the quick answer. Seems obvious and web searches will yield a plethora of sites that show trigonometry in surveying, but those surveyors have some deeper equations embedded into their programs. Mollweide's Formula is one of them. If you look at this equation, how many angles and how many sides of a given triangle are included in the formula? Why, from a number theory standpoint, would this be a good thing for surveyors -- what would they use it for? AND .....do you really think that the typical joe or jane surveyor would know this formula or even know of the existence of this formula?
Doctors. Particularly, radiologists use trig as they aim gamma rays into the bodies of their patients to eliminate tumors without traditional scalpels. How do you think trig is used in this area? Orthopedists use angles in their work, just check out the abstract to this article: http://www.ncbi.nlm.nih.gov/pubmed/7610093 or do a search -- there's lots available. Some images are not for those with a weak stomach.
Sailors. Just look for the triangles.
Rock Climbers and outdoor enthusiasts. Tyrolean Traverses (Can you find the triangles, angles to measure....?)
Astronomers....
You get the idea. In high school college-prep mathematics, trigonometry is often the first place students see direct applications of math in a variety of concrete areas. For your blog, find an application, a single application so you can develop it well, anything, and explain how trigonometry or the study of triangles applies to the field. Go ahead, ask parents, your friends' parents, anyone. Do they use trigonometry? Where? How? You might find lots of people who say, "Nope, never used it." Your mission is to find an application in the professional world.
Trigonometry has many uses today, but was historically developed for astronomy and geography over 2000 years ago! Astronomers at the time thought that the stars were fixed on an enormous sphere, and only the planets moved. The trigonometry they used was slightly different than what we're learning; it's called spherical trigonometry, which can also be used in geographic navigations.
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One use of trig in astronomy is being able to find the distance from Earth to a star. Since the Earth orbits the sun once a year, at six month intervals we're looking at the star from the two points of an isosceles triangle. (One point is where we are in, say, January; the other is where we would be in July.) We can find the vertex angle of the isosceles triangle by observing how far the star appears to move with respect to background galaxy, and since the base of the triangle is the diameter of Earth's orbit, we can find the height of the triangle, and therefore the distance from the star, using the tangent of the vertex angle.
http://curious.astro.cornell.edu/question.php?number=475
Another, related application of trigonometry is in geography. We can use it to find where places are in relation to others. Say point A and point B are 100 miles apart in one direction, and point B and point C are 120 miles apart in another direction. If we were to draw straight lines between these points, the angle at B would measure 31 degrees. We could find the distance between points A and C by applying the law of cosines. Incidentally, that distance comes out to be about 62 miles.
I sometimes wonder when it is that I'm going to use the math that I'm learning. In some professions, it's used on a near-daily basis!
Civil engineers use trigonometry to calculate distances so that they can figure out how long beams and rafters should be, etc. They also need to understand the forces of gravity on a structure.
ReplyDeleteTrigonometry, the study of triangles, has been used for thousands of years by sailors and for astronomy. It helped to determine where you were located on the earth, and sailors needed to be very sharp in its functions.
ReplyDeleteWhile there are many common applications of trigonometry, one particularly important job which utilizes trig is architecture, which focuses on building structures and designing. These structures need to be stable and safe, and without trigonometry, architects would not be able to effectively build anything.
Some examples where trigonometry is used in architecture are suspension bridges, domes, and support beams.
One of the most important professions that use trigonometry is architecture. Trigonometry is excessively important in architecture because architects use it to calculate distances. The architects especially use sine, cosine, and tangent to calculate distances that involve triangles. Architects also use cotangent, secant, and co-secant but not to the extent that they use sine, cosine, and tangent.
ReplyDeleteThese Trig functions are important because the architect can find opposite, adjacent, or hypotenuse values of any building containing triangular structures. Here is an example in which architects use trig: Architects needs to find out how high a crane should be in order to reach a certain height of a buiding. They can find this by using one of the six trig functions.
My first taught after treading the article was that Architects and Builders use trigonometry all the time, but then I read the other comments and realized that everyone else thought so as well. So, I want to talk about how furniture designers and builders use trigonometry as well. Every carpenter does, whether they know it or not, when they're measuring angles of the wood joints. But, some furniture designers use trig even deeper, such as the person who built this masterpiece: http://www.radiusfurniture.blogspot.com/?m=1. The craftsman who built that table calls his work "radius design" and usually his pieces consist of parts an origin, just like in trig! I think this is a really cool example of how trig is used in an uncommon field
ReplyDeleteOne example of trigonometry that comes quickly to mind is navigation. In class we have been doing some problems involving navigation and it also makes a lot of sense in the real world to. If two boats know their initial distances from a single point and the angle between these two distances, they can use the law of cosines to find the shortest distance between themselves. Trigonometry is used to pinpoint single locations. Though we have many pieces of technology to find our locations now, trigonometry was depended on by sailors and architects for thousands of years. It really interesting to apply the things we learn in math class everyday to our world and prove that what we are learning will make a difference some day.
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