Trigonometry

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

The 3rd-century astronomers first noted that the lengths of the sides of a right-angle triangle and the angles between those sides have fixed relationships: that is, if at least the length of one side and the value of one angle is known, then all other angles and lengths can be determined algorithmically. These calculations soon came to be defined as the trigonometric functions and today are pervasive in both pure and applied mathematics: fundamental methods of analysis such as the Fourier transform, for example, or the wave equation, use trigonometric functions to understand cyclicalphenomena across many applications in fields as diverse as physics, mechanical and electrical engineering, music and acoustics, astronomy, ecology, and biology. Trigonometry is also the foundation of surveying.

Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.

Trigonometry basics are often taught in schools, either as a separate course or as a part of a precalculus course.

Main article: Trigonometric function

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

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

• Cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse.

${\displaystyle \cos A={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}={\frac {b}{\,c\,}}\,.}$

• Tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg.

${\displaystyle \tan A={\frac {\textrm {opposite}}{\textrm {adjacent}}}={\frac {a}{\,b\,}}={\frac {a}{\,c\,}}*{\frac {c}{\,b\,}}={\frac {a}{\,c\,}}/{\frac {b}{\,c\,}}={\frac {\sin A}{\cos A}}\,.}$

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

${\displaystyle \csc A={\frac {1}{\sin A}}={\frac {\textrm {hypotenuse}}{\textrm {opposite}}}={\frac {c}{a}},}$

${\displaystyle \sec A={\frac {1}{\cos A}}={\frac {\textrm {hypotenuse}}{\textrm {adjacent}}}={\frac {c}{b}},}$

${\displaystyle \cot A={\frac {1}{\tan A}}={\frac {\textrm {adjacent}}{\textrm {opposite}}}={\frac {\cos A}{\sin A}}={\frac {b}{a}}.}$

Interesting facts

Words such as formula, equation and calculation sounds boring for those who hate Maths as a subject, whereas it is fun for those who have keen interest towards solving equations/problems.

October 14th is celebrated as World Maths Day. Let us know some interesting and amazing facts about Mathematics.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.
2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion
3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D
4. 2 and 5 are the only primes that end in 2 or 5
5. An icosagon is a shape with 20 sides

Amazing Facts About Maths

Words such as formula, equation and calculation sounds boring for those who hate Maths as a subject, whereas it is fun for those who have keen interest towards solving equations/problems.

October 14th is celebrated as World Maths Day. Let us know some interesting and amazing facts about Mathematics.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.
2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion
3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D
4. 2 and 5 are the only primes that end in 2 or 5
5. An icosagon is a shape with 20 sides

Amazing Facts About Maths

Words such as formula, equation and calculation sounds boring for those who hate Maths as a subject, whereas it is fun for those who have keen interest towards solving equations/problems.

October 14th is celebrated as World Maths Day. Let us know some interesting and amazing facts about Mathematics.

1. Zero ( 0 ) is the only number which can not be represented by Roman numerals.
2. What comes after a million, billion and trillion? A quadrillion, quintillion, sextillion, septillion, octillion, nonillion, decillion and undecillion
3. Plus (+) and Minus (-) sign symbols were used as early as 1489 A.D
4. 2 and 5 are the only primes that end in 2 or 5
5. An icosagon is a shape with 20 sides

Fun and Interesting facts about Numbers

Fun and interesting facts:

0 - Zero was not even considered a number for the Ancient Greeks. However, they also questioned whether 1 was a number.

1 – The number 1 is NOT prime number, as many people believe. It is also the exact amount of butler schools in the US and the number of public telephones in Kabul.

Square root 2 (or 1.41...) - … is also called Pythagoras' constant. Paper sizes (A4, A3 etc.) are all based on a single aspect ratio of the square root of two.

1.618… - The golden ratio between two quantities (such as lengths) often appears in nature (tree branches, uncurling ferns, pine cone arrangements, etc.) and has been used throughout history to create aesthetically pleasing designs and art works such as Leonardo da Vinci’s Mona Lisa. It’s even used in analysing modern financial markets.

4 - The four-second rule is the amount of time that internet user will wait for a page to load before leaving and going to another site. And a dollar bill can be double folded (forward and backwards) 4x103 times before it will tear.

5 – The number of baseball gloves that can be made from one cow.

9 - A paper cannot be folded more than 9 times. Try it!

13 - One of the most widespread superstitious beliefs is that the number 13 is unlucky. So common is this that many hotels and office buildings in Europe and the United States do not have a room number 13 or a floor 13.