Trigonometry

Trigonometry was probably developed for use in sailing as a navigation method used with astronomy.[2] The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago.[citation needed] The common practice of measuring angles in degrees, minutes and seconds comes from the Babylonian's base sixty system of numeration. The Sulba Sutras written in India, between 800 BC and 500 BC, correctly computes the sine of (=45°) as in a procedure for "circling the square" (i.e., constructing the inscribed circle).[citation needed]

The first recorded use of trigonometry came from the Hellenistic mathematician Hipparchus[1] circa 150 BC, who compiled a trigonometric table using the sine for solving triangles. Ptolemy further developed trigonometric calculations circa 100 AD.

The ancient Sinhalese in Sri Lanka, when constructing reservoirs in the Anuradhapura kingdom, used trigonometry to calculate the gradient of the water flow. Archeological research also provides evidence of trigonometry used in other unique hydrological structures dating back to 4 BC.[3]

The Indian mathematician Aryabhata in 499, gave tables of half chords which are now known as sine tables, along with cosine tables. He used zya for sine, kotizya for cosine, and otkram zya for inverse sine, and also introduced the versine. Another Indian mathematician, Brahmagupta in 628, used an interpolation formula to compute values of sines, up to the second order of the Newton-Stirling interpolation formula.

In the 10th century, the Persian mathematician and astronomer Abul Wáfa introduced the tangent function and improved methods of calculating trigonometry tables. He established the angle addition identities, e.g. sin (a + b), and discovered the sine formula for spherical geometry:

Also in the late 10th and early 11th centuries, the Egyptian astronomer Ibn Yunus performed many careful trigonometric calculations and demonstrated the formula

.

Indian mathematicians were the pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha (circa 1350-1200 BC) is the first person thought to have used geometry and trigonometry for astronomy, in his Vedanga Jyotisha.

Persian mathematician Omar Khayyám (1048-1131) combined trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means. Khayyam solved the cubic equation x3 + 200x = 20x2 + 2000 and found a positive root of this cubic by considering the intersection of a rectangular hyperbola and a circle. An approximate numerical solution was then found by interpolation in trigonometric tables.

Detailed methods for constructing a table of sines for any angle were given by the Indian mathematician Bhaskara in 1150, along with some sine and cosine formulae. Bhaskara also developed spherical trigonometry.

The 13th century Persian mathematician Nasir al-Din Tusi, along with Bhaskara, was probably the first to treat trigonometry as a distinct mathematical discipline. Nasir al-Din Tusi in his Treatise on the Quadrilateral was the first to list the six distinct cases of a right angled triangle in spherical trigonometry.

In the 14th century, Persian mathematician al-Kashi and Timurid mathematician Ulugh Beg (grandson of Timur) produced tables of trigonometric functions as part of their studies of astronomy.

The mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in 1595 which may have coined the word "trigonometry".

One half base times height of the triangle times length of the prism.

No, you're just subracting basically. It' the same as -2 + (-2). The answer is -4, and it's a negative plus a negative. Or, if you'd rather: If you owe someone money, and then add another debt, does your debt not grow?

And Love, I'd suggest that unless you're in the sixth grade or lower, you not only get tutored in math, but in English and spelling as well. [Does]

It's an equilateral triangle whose legs are all 90-degree arcs.

Here's a quadrantal triangle on the earth:

-- Start at the north Pole.

-- Draw the first side, down along the north 1/2 of the Prime Meridian to the equator.

-- Draw the second side westward along the equator, to 90 degrees west longitude.

-- Draw the third side straight north, back up to the north Pole.

Each side of the triangle is 90 degrees, each interior angle is also 90 degrees,

and the sum of its interior angles is 270 degrees.

Pretty weird.

6

arabics

If the coordinates of the three vertices are (xa, ya), xb, yb) and (xc, yc) then the coordinates of the centroid are [(xa+xb+xc)/3, (ya+yb+yc)/3].

Repetitive behavior can be described by a point moving in a circle. The time of repetition is equivalent to time taken by that particle to complete that circle. When the point moves in a circle, its angle changes from 0 to 360 degrees; all of these values can be given by a sine function or a cosine function.

what are the parts of the Cartesian plane ?

The diameter was 26 cm.

Sine Theta (sin θ) = opposite/hypotenuse = a/c

Cosine Theta (cos θ) = adjacent/hypotenuse = b/c

Tangent Theta (tan θ) = opposite/adjacent = a/b

Cotangent Theta (cot θ) = adjacent/opposite = b/a

Secant Theta (sec θ) = hypotenuse/adjacent = c/b

Cosecant Theta (csc θ) = hypotenuse/opposite = c/a

You may need to look on the link below for some sample calculations

cos(79) = 0.1908, approx.

The vertex is the singular of vertices and they both have angles that are measured in degrees.

you need to have at least 2 values of the lengths of the triangle

and then you can find the angle by sine, cosine or tangent formulas

you may try this online calculator for right triangles.

http://www.rillocenter.com/calculate/trigonometry.html

The cosine of 35 degrees is 0.82, to the same number of significant digits as 35.

it is 0because on the unit circle 270 is the negative y axis (0,1) the x coordinate is the cos value

No, they are functions associated with angle values. The function values are dependent on the input angle.

hipparchus

First since I don't know how to type in the square root of something, I'm going to type it in like this: sqrt(x)

Now say you have 1/sqrt(3). The square root can not be on the bottom. So mulitply the equation by the sqrt(3). This means TOP and BOTTOM! so then it looks like sqrt(3)/3. And that is an acceptable answer.

There is no set number of items in a unit. Often a unit will be 6, 12, 24, or 36 but it can be any amount.

cot(360°) = cot(0°) = tan(90°) = ∞

It can easily be measured by using a protractor and measuring the angle between the ground and the top of the tree. You need to know exactly how far you are from the tree. Then you can use trigonometry to calculate the height of the tree. Tan (angle in degrees) = height of tree / distance from tree

A force of 36.06 N, at 33.69 degrees up from East.

The question has no answer.
This sort of question is based on the assumption that gravitational acceleration is 9.8 m/s^2 (downwards). In that case, if the rock is projected from the ground its height at time t is 24t - 4.9t^2. It cannot be greater than that unless air resistance is negative!