Arithmatics, Mathematics

Arithmatics

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics. It consists of the study of numbers, especially the properties of the traditional operations between them—addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are sometimes still used to refer to a wider part of number theory

Totally dependent on the operation of Addition,Subtraction, Multiplication and Division.

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Mathematics, Trigonometry

Trigonometry/Function

If one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined, except for similarity, by the angles. Once the angles are known, the ratios of the sides are determined, regardless of the overall size of the triangle. If the length of one of the sides is known, the other two are determined. These ratios are given by the following trigonometric functions of the known angle A, where a, b and c refer to the lengths of the sides in the accompanying figure:

  • Sine function (sin), defined as the ratio of the side opposite the angle to the hypotenuse.

    245px-TrigonometryTriangle.svg

\sin A=\frac{\textrm{opposite}}{\textrm{hypotenuse}}=\frac{a}{\,c\,}\,.

  • Cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.
\cos A=\frac{\textrm{adjacent}}{\textrm{hypotenuse}}=\frac{b}{\,c\,}\,.
  • Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.
\tan A=\frac{\textrm{opposite}}{\textrm{adjacent}}=\frac{a}{\,b\,}=\frac{a}{\,c\,}*\frac{c}{\,b\,}=\frac{a}{\,c\,} / \frac{b}{\,c\,}=\frac{\sin A}{\cos A}\,.

The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A. The adjacent leg is the other side that is adjacent to angle A. The opposite side is the side that is opposite to angle A. The terms perpendicular and base are sometimes used for the opposite and adjacent sides respectively. Many people find it easy to remember what sides of the right triangle are equal to sine, cosine, or tangent, by memorizing the word SOH-CAH-TOA (see below under Mnemonics).

The reciprocals of these functions are named the cosecant (csc or cosec), secant (sec), and cotangent (cot), respectively:

\csc A=\frac{1}{\sin A}=\frac{\textrm{hypotenuse}}{\textrm{opposite}}=\frac{c}{a} ,
\sec A=\frac{1}{\cos A}=\frac{\textrm{hypotenuse}}{\textrm{adjacent}}=\frac{c}{b} ,
\cot A=\frac{1}{\tan A}=\frac{\textrm{adjacent}}{\textrm{opposite}}=\frac{\cos A}{\sin A}=\frac{b}{a} .
To know more about….see another Post……


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Facts and figure, Knowledge, Science

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The southern part of Orion, the famous constellation and mythical hunter, appears quite picturesque posing here over a famous volcano. Located in the Canary Islands off the northwest coast of Africa, the snow-peaked Teide is one of the largest volcanoes on Earth. Lights from a group planning to summit Teide before dawn are visible below the volcano’s peak. In this composite of exposures taken from the same location one night last month, the three iconic belt stars of Orion are seen just above the peak, while the famous Orion Nebula and the rest of Orion’s sword are visible beyond the volcano’s left slope. Also visible in the long duration sky image are the Horsehead Nebula, seen as a dark indentation on the red emission nebula to the belt’s left, and the Flame Nebula, evident just above and to the right of the Horsehead.

Prof.Rajeev Tripathi

Astronomy, Facts and figure, Knowledge

Astronomy,Knowledge,Space

How massive can a normal star be? Estimates made from distance, brightness and standard solar models had given one star in the open cluster Pismis 24 over 200 times the mass of our Sun, making it one of the most massive stars known. This star is the brightest object located just above the gas front in the featured image. Close inspection of images taken with the Hubble Space Telescope, however, have shown that Pismis 24-1 derives its brilliant luminosity not from a single star but from three at least. Component stars would still remain near 100 solar masses, making them among the more massive stars currently on record. Toward the bottom of the image, stars are still forming in the associated emission neb

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ula NGC 6357. Appearing perhaps like a Gothic cathedral, energetic stars near the center appear to be breaking out and illuminating a spectacular cocoon.

Prof.Rajeev Tripathi

Mathematics

Algebra

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Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.

Mathematics


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Astronomy

Conservation of Energy

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Astronomy

Watch “INTRODUCTION by Prof. Rajeev Tripathi” on YouTube

INTRODUCTION by Prof. Rajeev Tripathi: https://youtu.be/uvzL25ncRH8

Astronomy

Watch “INTRODUCTION by Prof. Rajeev Tripathi” on YouTube

INTRODUCTION by Prof. Rajeev Tripathi: http://youtu.be/uvzL25ncRH8

Astronomy

Astronomy

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What strange world is this? Earth. In the foreground of the featured image are the Pinnacles, unusual rock spires in Nambung National Park in Western Australia. Made of ancient sea shells (limestone), how these human-sized picturesque spires formed remains unknown. In the background, just past the end of the central Pinnacle, is a bright crescent Moon. The eerie glow around the Moon is mostly zodiacal light, sunlight reflected by dust grains orbiting between the planets in the Solar System. Arching across the top is the central band of our Milky Way Galaxy. Many famous stars and nebula are also visible in the background night sky. The featured 29-panel panorama was taken and composed last September after detailed planning that involved the Moon, the rock spires, and their corresponding shadows. Even so, the strong zodiacal light was a pleasant surprise.