Trigonometry

At 24 years of age, he wrote a book called Disquisitines Arithmeticae, which is regarded today as one of the most influential books written in math.

He also wrote the first modern book on number theory, and proved the law of quadratic reciprocity.

In 1801, Gauss discovered and developed the method of least squares fitting, 10 years before Legendre, unfortunately, he didn't publish it.

Gauss proved that every number is the sum of at most three triangular numbers and developed the algebra of congruences.

Surveyors use trigonmetry to find the exact height, length, and/or width of man-made and/or natural objects without having to measure it all manually. I think, to get the angle, they use a special gun thing that they point at the end of the object, which works it all out, then they just have to measure the distance they are from the object. After that its up to their trigonometry skills, and if they're good, then they should find the almost exact length, height, and/or width.

There are so many jobs that use trigonometry -> an architect, Crime Scene Investigators, any job dealing with outer space (astronomers, physicist, astronauts, the men that guide the astronauts, etc), carpenter, machinist, engineering (mechanical, computer, chemical, civil, aeronautical, industrial, etc.), any job involving navigation (pilots -- air and sea), computer game creators. The list could go on and on, but I think you get the idea.

there many jobs that have to uses trigonometrysuch as a carpentry , law and order these jobs have to use trigonometry because for carpentry if you don't use it then you might as well not use it any ways and you Can also use it to impress the boss you know mabye get a little raise in your money but really when you are cutting out an angle you have to use trigonometry, also architecture uses trigonometry so they can figure out how to build the complex shapes that modern buildings require

Base times Width times height. Take the measurement of the base, multiply it by the measurement of the width and multiply it all again by the measurement of the height. B*W*H=Cube

another way of saying it:

volume: multiply the length times the length times the length. Surface area: length times width times six.

There are two ways to solve for the double angle formulas in trigonometry. The first is to use the angle addition formulas for sine and cosine.

* sin(a + b) = sin(a)cos(b) + cos(a)sin(b) * cos(a + b) = cos(a)cos(b) - sin(a)sin(b) if a = b, then

* sin(2a) = sin(a)cos(a) + cos(a)sin(a) = 2sin(a)cos(a) * cos(2a) = cos2(a) - sin2(b) The cooler way to solve for the double angle formulas is to use Euler's identity. eix = cos(x) + i*sin(x). Yes, that is "i" as in imaginary number.

we we put 2x in for x, we get

* e2ix = cos(2x) + i*sin(2x) This is the same as

* (eix)2 = cos(2x) + i*sin(2x) We can substitute our original equation back in for eix.

* (cos(x) + i*sin(x))2 = cos(2x) + i*sin(2x) We can distribute the squared term.

* cos2(x) + i*sin(x)cos(x) + i*sin(x)cos(x) + (i*sin(x))2 = cos(2x) + i*sin(2x) And simplify. Because i is SQRT(-1), the i squared term becomes negative.

* cos2(x) + 2i*sin(x)cos(x) - sin2(x) = cos(2x) + i*sin(2x) * cos2(x) - sin2(x) + 2i*sin(x)cos(x) = cos(2x) + i*sin(2x) Now you can plainly see both formulas in the equation arranged quite nicely. I don't yet know how to get rid of the i, but I'm working on it.

In a right-angled triangle, the hypotenuse is the longest side, opposite the right-angle. There are two ways of finding the length of the hypotenuse using mathematics: Pythagoras' theorem or trigonometry, but for both you need either two other lengths or an angle.

For Pythagoras' theorem, you need the other two lengths. The theorem is a2+b2=c2, or the square root of the sum of two angles squared, where c=the hypotenuse. Let's say that one length is 4.8cm and the other 4cm. 4.82+42=6.22. So, the answer is 6.2cm.

If you have one side and one angle, use trigonometry. You will need a calculator for this. Each side of the right-angled triangle has a name corresponding to the positioning of the angle given. The opposite is the side opposite the given angle, the adjacent is the side with the right-angle and the given angle on it, and the hypotenuse is the longest side or the side opposite the right-angle. There are three formulas in trigonometry: sin, cos and tan. Sin is the opposite/hypotenuse; cos is the adjacent/hypotenuse; and tan is the opposite/adjacent. As we are trying to find the hypotenuse, we already have either the opposite or the adjacent, and one angle. Let's say that our angle is 50o and we have the adjacent side, and that is 4cm. So, we have the adjacent and want to know the hypotenuse. The formula with both the adjacent and the hypotenuse in is cos. So, Cos(50o)=4/x where x=hypotenuse. We can single out the x by swapping it with the Cos(50o), so x=4/Cos(50o) -> x=6.22289530744164. This is the length of the hypotenuse, and is more accurate that Pythagoras' theorem.

you use the the 3 trigonometry functions , sin=opposite divided by hypotenuse cos=adjacent divided by hypotenuse tan=opposite divided by adjacent these are used to work out angles and side lengths in right angle triangles only!!! sine,cosine,tangent :)

To convert from decimal to percentage, you times 100.

2.3 * 100 = 230%

It isn't clear in what form you have the complex number. But you can change it from the form (absolute value, angle) to the form (real part + imaginary part) using the polar-rectangular conversion available on scientific calculators (and the other way round, with the rectangular-polar conversion). Note that a complex number in the form (real part + imaginary part) is most appropriate for addition and subtraction, while a complex number of the form (absolute value, angle) is most appropriate for multiplication or division, so depending on the operations, you may want to convert back and forth several times.

Depending on your career, you may or may not need trigonometry. If your job does not require a lot of math, it is unlikely that you will use trigonometry very often, however, this is not a reason not to study it. The skills and discipline developed in your trigoometry class will help you no matter what career you choose.

Basic trigonometry - angles or side-lengths of right-angled triangles - is quite common in many practical applications, and not just professionally.

Surveying uses the more complex, as well as basic, trig rules.

However, trigonometry as such is found in all manner of fields. For example, in electronics, sound & vibration studies, analysing wave behaviour and characteristics is very largely trigonometrical because the "shape" of a basic sound-wave, simple alternating-current electricity or indeed ocean swell is a sine function.

No.

sin(60 degrees) = 0.8660 approx. The exact value is sqrt(3)/2.

Trigonometry originated in ancient times, and was closely related to geometry. It was useful especially in astronomy and navigation.

Later on trigonometry led to the idea of sine waves as fundamental for analysing vibrations of all kinds. Trigonometric functions occur in the theory of complex numbers, and now the trig functions turn up in many places in mathematics and its applications, from optics to the theory of alternating current in electrical engineering. The uses of the trig functions have spread far beyond the original ones.

1

Substitute that value of the variable and evaluate the polynomial.

Mathematics is a subject that is vital for gaining a better perspective on events that occur in the natural world. A keen aptitude for math improves critical thinking and promotes problem-solving abilities. One specific area of mathematical and geometrical reasoning is trigonometry which studies the properties of triangles. Now it's true that triangles are one of the simplest geometrical figures, yet they have varied applications. The primary application of trigonometry is found in scientific studies where precise distances need to be measured.

The techniques in trigonometry are used for finding relevance in navigation particularly satellite systems and astronomy, naval and aviation industries, oceanography, land surveying, and in cartography (creation of maps). Now those are the scientific applications of the concepts in trigonometry, but most of the math we study would seem (on the surface) to have little real-life application. So is trigonometry really relevant in your day to day activities? You bet it is. Let's explore areas where this science finds use in our daily activities and how we can use this to resolve problems we might encounter. Although it is unlikely that one will ever need to directly apply a trigonometric function in solving a practical issue, the fundamental background of the science finds usage in an area which is passion for many - music! As you may be aware sound travels in waves and this pattern though not as regular as a sine or cosine function, is still useful in developing computer music. A computer cannot obviously listen to and comprehend music as we do, so computers represent it mathematically by its constituent sound waves. And this means that sound engineers and technologists who research advances in computer music and even hi-tech music composers have to relate to the basic laws of trigonometry.

A rhombus has four equal sides but not necessarily equal angles. but tht is all i got

Calculus

Trigonometry is used very extensively in engineering. It is used to break force vectors into components, allowing civil and construction engineers to see how stress is channeled throughout a building. It is used to model sound and light waves, which is a useful tool for acoustic and optic engineers. It is also used extensivly in electrical engineering to find the strengths of fields.

[deltay]/[deltax]

If you don't understand that:

y1-y2/x1-x2

Depending on your career, you may or may not need trigonometry. If your job does not require a lot of math, it is unlikely that you will use trigonometry very often, however, this is not a reason not to study it. The skills and discipline developed in your trigoometry class will help you no matter what career you choose.

Lemma

Trigonometry is used in the fields of design, music, navigation, cartography, manufacturing, physics, optics, projectile motion, and any other field which involves angles, fields, waves, harmonics, and vectors.

Simply put, a vector is 2 dimensional.

Think of speed - it is only one dimensional. It is not a vector, it is a scalar. It is measured in a scale, most commonly noticed when inside a vehicle. You are travelling at 100km/h (60mph)

Vectors are 2 dimensional, they have a magnitude and a direction.

Think of velocity, as an arrow - imagine you are travelling at 60 mph in a northerly direction, your arrow would be pointing to the notth, with a magnitude of 60mph, If you were travelling at 60mph in a southerly direction, your velocity vector would be pointing towards the south, the exact opposite of your vector if you were travelling in a northerly direction.

However the speed in these two scenario's, speed not being a vector, remains exactly the same, 60mph.