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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 shape is a trapezium?

A trapezium is a shape with four sides. Of these, one pair of sides are parallel. The only restriction on the other pair is that they are not parallel (because you then have a parallelogram).

What are the scopes of trigonometry?

Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angles of triangles, and with trigonometric functions, which describe those relationships and angles in general, and the motion of waves such as sound and light waves.

There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets, electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology), seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering, mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

What jobs require that you know trigonometry?

Architect, they need to know trigonometry functions, among others they utilize to find the size of unknowns parts of shapes.

Surveyors, carpenters.

Trig is not restricted to angles, it has huge applications in waves, and occurs frequently as solutions to certain common differential equations. It is needed by any job that uses math. Thus, all engineers need trig, and it would be beneficial to any person who pursues science.

What is euler's formula?

Euler's formula states that, for any real number x,

eix = cos x + i sin x

where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians.

[Sources:]

[1] My own knowledge.

[2] linked

Multi sided shape?

Placing a question mark at the end of a phrase does not make it a sensible question. Try to use a whole sentence to describe what it is that you want answered. The answer may be "polygon" but it is difficult to tell when the question is unclear.

How do you calculate radius?

Radius is calculated by dividing diameter by two.

Measure the distance across the circle then divide it in half for example:

You measure the distance across the circle (the diameter) = 6,

then 6 divided in half, the radius is 3.

How do you calculate ratio?

current ratio = current assets / current liablities A ratio (in trig) is simply the division of two lengths. A tangent (in trig) is the ratio of the opposite and adjacent legs.

How many faces does a cube have?

A cube has six faces. Here is some more information about cubes.

A cube is a 3-dimensional polyhedron with 6 square faces.

Each vertex, or pointer corner, is occurs where three sides meet.

A cube has 12 edges and 8 vertices.

Another name for a cube is a regular hexahedron.

A cube is one of 5 platonic solids.

How do you find the angle of elevation of the sun if the shadow of the pole 60 ft tall reaches 92 ft from the pole?

Providing that the pole is on level ground you have the outline of a right angled triangle with an adjacent side of 92 ft (the shadow of the pole) and a opposite side of 60 ft (the height of the pole). To find the angle of elevation use the tangent ratio. Tangent = Opposite/Adjacent Tangent = 60/92 = 0.652173913 Tan-1(0.652173913) = 33.11134196 degrees Therefore the angle of elevation is 33o correct to two significant figures.

What kind of symmetry does an even function have?

A function f(x) is even if f(-x) = f(x). A graph of f(x) would be symmetric about the y-axis (vertical symmetry about x=0). f(x) need not be "well-behaved" or even continuous, unlike the examples given in Wikipedia article on "Even and odd functions". The article does make this clear - under "Some facts".

What equals 1 - cos squared x divided by cos squared x?

tan^2(x)

Proof:

cos^2(x)+sin^2(x)=1 (Modified Pythagorean theorem)

sin^2(x)=1-cos^2(x) (Property of subtraction)

cos^2(x)-1/cos^2(x)=?

sin^2(x)/cos^2(x)=? (Property of substitution)

sin(x)/cos(x) * sin(x)/cos(x) = tan(x) * tan(x) (Definition of tanget)

= tan^2(x)

How do you solve csc x sin x equals cos x cot x plus?

Suppose csc(x)*sin(x) = cos(x)*cot(x) + y

then, ince csc(x) = 1/sin(x), and cot(x) = cos(x)/sin(x),

1 = cos(x)*cos(x)/sin(x) + y

so y = 1 - cos2(x)/sin(x) = 1 - [1 - sin2(x)]/sin(x) = [sin2(x) + sin(x) - 1]/sin(x)

Which ratios correctly describes the cosine function?

The cosine function on a right triangle is Adjacent leg divided by the hypotenuse of the triangle.

What is the cosine of 55 degrees?

0.5735764264 (nearest 10 decimal places).

What is sec theta if sin theta equals 2 over 3 with theta in quadrant 1?

sin(t) = 2/3

sin2(t) + cos2(t) = 1

so cos(t) = ± sqrt[1 - sin2(t)]

but because t is in the first quadrant, cos(t) > 0 so cos(t) = + sqrt[1 - sin2(t)]

= sqrt[1 - 4/9] = sqrt[5/9] = sqrt(5)/3

Then sec(t) = 1/cos(t) = 1/sqrt(5)/3 = 3/sqrt(5) = 3*sqrt(5)/5

How do trig functions communicate?

They do not. They are not animate nor sentient and so they are incapable of communicating.

What is the cosecant of 115 degrees?

Cosecant(115 deg) = 1/sine(115 deg) = 1/0.9063 = 1.1034