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Trigonometry

Trigonometry is a field of mathematics. It is the study of triangles. Trigonometry includes planar trigonometry, spherical trigonometry, finding unknown values in triangles, trigonometric functions, and trigonometric function graphs.

3,810 Questions

What is the formula for volume of a partial cylinder - my cylinder is horiz. w a 60'Dia 2'L and has 18'H full.?

v = lcos^-1 (1-(y/r))r^2+l sqrt[(2r-y)y](y-r)=pi (ry^2-(y^3/3))

where v=volume, y=height of liquid in tank, r=radius of tank, l=Length of tank

Or you can just use this:

http://grapevine.abe.msstate.edu/~fto/tools/vol/parthcylinder.html

Formula for a triangular prism?

The answer depends on formula for WHAT! Its surface area, number of edges, mass, volume. And since you have not bothered to share that crucial bit of information, I cannot provide a more useful answer.

Geometry in mathematics comes under pure mathematics or applied mathematics?

When you study the theory of geometry, it is pure mathematics.

However, when you start using the geometry you have learned in other, more practical areas, then it becomes applied.

How do you know if an equation is not linear?

Linear equations come in the form y=mx+b or y=mx-b, where x and y are the variables x and y and b is a constant (like 3). All other equations are non-linear.

Linear equations has a power of 1!

as long as the X has a power of 1, it is a linear equation.

What is the formula and solution of this problem an angle of 50 degrees in standard position has its terminal side in the first quadrant. find the coordinates of point P on the unit circle.?

This is somewhat difficult to explain without images, but here goes:

You can use the information given in the problem to draw a right triangle on your coordinate axes. The hypotenuse of this right triangle should extend from the origin to point P and make a 50 degree angle with the x-axis. We'll call this hypotenuse r, which in this case is 1 (because we're dealing with the unit circle). If you extend a line down from point P perpendicular to the x-axis, the segment formed, which we will call y, will be the side of the right triangle opposite the 50 degree angle. The remaining side, x, lies along the x-axis between the origin and the point where side y intercepts the x axis.

Recognize that side x and side y represent, respectively, the x and y coordinates of P. These values can be found using trigonometric relationships.

Recall that sin(a) = opposite/hypotenuse. In this case, a = 50, the opposite side is y, and the hypotenuse is r=1, so we can rewrite this equation as

sin(50) = y/r = y

Which means that y is simply sin(50).

Similarly, cos(a) = adjacent/hypotenuse, so cos(50) = x/r = x. x = cos(50).

P is therefore located at (cos[50], sin[50])

How does a trapezium look like?

A trapezium is a 4 sided quadrilateral with a pair of opposite parallel sides that have different lengths

What are the trigonometry functions?

sin(A)= opp./hyp.

cos(A)= adj./hyp.

tan(A)= opp./adj.

sin(A)= opp ÷ hyp

cos(A)= adj ÷ hyp

tan(A)= opp ÷ adj

For a diagram of what the sides of a right triangle are, go to http://upload.wikimedia.org/wikipedia/commons/4/4f/TrigonometryTriangle.svg.

Any 3D shape with a number of faces?

im 101% sure that the answer is a cuboid im a mathmetishion and i know my stuff real well. i hope this helps you with any homework given to you and in the meantime farewell.

Why was cartesian coordinate system invented?

It allowed points in space to be described algebraically. This allowed lines and curves to be described using algebra. Bringing together algebra and geometry meant that tools that mathematicians had developed for solving algebraic problems could be applied to problems in geometry and tools from geometry could be applied to algebra.

What is the value of sin 20?

0.34202014332566873304409961468226

By using trigonometric identities find the value of sin A if tan A a half?

The value of tan A is not clear from the question.

However, sin A = sqrt[tan^2 A /(tan^2 A + 1)]

The point where the x and y-axis meet?

The point where the x-axis and the y-axis meet is called the origin.

What is the origin of trigonometry As in a person time period or area?

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 (India), 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 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.[citation needed] 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 : 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" itself. Hope that helps. :)

How do you solve an equation that uses spherical trigonometry without a calculator?

Before calculators, trig functions in general were evaluated using a slide rule (fast, but accurate to only 2-3 significant digits, and interpolation tables, which required interpolating between values in a printed table of function values to get up to 3-4 significant digits. Tricks were a big part of the repertoire - for example for small angles of less than about 7 degrees, sin and tangent are equal to the angle in radians.

Spherical geometry was fairly labor intensive, to say the least, since several trig functions are used for even simple distance and angle calculations. Special tables were printed for common cases, such as plotting great circle distances and bearings for terrestrial navigation.

In a desert island setting, given infinite time and desire, trig functions can be calculated using various converging series, with the Taylor series being a commonly taught (though slow!) example.