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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

Surface area formula?

The answer depends on the shape whose surface area for which a formula is required.

What are the formulas that include the changes of degree to radian?

To convert from degrees to radians, multiply the number of degrees by (pi / 180). Pi is approximately 3.1416.

How to determine all possible solutions to two decimal places for sin 3x equals negative sqrt 3 over two?

sin(3x) = -sqrt(3)/2

so 3x = 240 + k*360 degrees or 300 + k*360 degrees where k is any integer

so that x is 80+120k or 100+120k degrees.

Where does the word railroad come from?

Railroad and railway are both words referring to 'tracked' roads, where a guides (rails) keep the wheeled vehicle on a specific route. The earliest known reference to the word "railroad" is in 1757 and referred to a mine tram on wooden rails and moved either by animals or men. Tracked tramways have been around since antiquity.

The usage for modern railroads hauling freight and people is from the 1820's.

Railroad is a typical American English usage. Railway is more typical British American usage. However there is considerable crossover is usage. For example the "South Pacific Railway Company" (1887) was originally incorporated as the "South Pacific Railroad Company" (1876).

The

How are cranes removed from the roof of tall buildings?

From what I have read: The crane "grows" using a jib, hydraulics, and sections. When the building is completed, the arms are dissassembled on the roof (they may be removed by another crane attached to a truck, or by other equipment on the roof?), and the process is then reversed (each section removed floor by floor by equipment inside the building). The jib is lowered as each section is removed, until there is nothing left, and the jib assembly is removed at ground level. I may need correction on this one though

Is a sine function a periodic function?

Yes, the sine function is a periodic function. It has a period of 2 pi radians or 360 degrees.

Who is sonya kovalevsky?

"Sonya Kovalevsky (1850-1891) was a Russian mathematician. She received her Ph.D from the University of Gottingen for her thesis on partial differential equations. In 1888 she won the Bodin Prize for her memoir on the rotation of a solid body about a fixed point." Excerpted from the Columbia Encyclopedia, 6th. Edition 2007

What is the origin of the word is?

Check any good dictionary (not a small paperback). The word has roots that include Old High German "ist", Old Norse "es", Gothic "ist", Latin "est, and the infinitive esse", Greek "esti", Sanskrit "asti", and Hittite "aszi". A wonderful lineage for such an unassuming [and powerful] word.

What does pricipal mean in math?

calculate the volume of a cylindrical drum 18 cm in diameter 56 in deep

How do you calculate the freq of a sine wave?

Suppose a sine wave of the form y = A*sin(k) with

  • A = amplitude or maximum value of the function y (namely when k = pi/2 or 90°)
  • k = the value on the x-axis of the function

It's typical of a sine wave that it's periodic, which means the function y repeats itself after a certain period. This period is equal to 2*pi or 360°, for example:

for k = pi/2, 5*pi/2, 9*pi/2, ... the value of y will be the same and equal to A (notice that 5*pi/2 = pi/2 + 2*pi and 9*pi/2 = 5*pi/2 + 2*pi)

In physics it's a more common practice to write a sine wave as y = A*sin(omega*t) with omega the angular frequency specified in radians/s (omega refers to the Greek letter) and t the time specified in seconds.

Now, when you want to calculate the frequency f of a sine wave (which is not equal to the angular frequency) or in other words the number of complete cycles that occur per second (specified in cycle/s or s-1 or Hz), you need to know the time T required to complete one full cycle (specified in s/cycle or just s or Hz-1). The frequency f is then equal to 1/T.

Knowing omega you can calculate the frequency in a different and more common way:

since the sine wave is periodic and after a time T one cycle has been completed (thus one period), it follows that omega*T = 2*pi for the function y to have the same value after one period (the function y having the same value is equal to completing one cycle).

Let's rearrange this formula by bringing 2*pi to the left and T to the right, so we get:

omega/(2*pi) = 1/T and since 1/T = f we finally get:

f = omega / (2*pi)

How many different types of triangle are there?

For the "catch all" and most broad type of triangles, there are 3:

Obtuse - 1 angle > 90°

Acute - all angles < 90°

Right - 1 angle exactly 90°

There are more specific categories, such as isosceles triangles, which can be obtuse, right or acute triangles that contain exactly 2 angles of equal degree, and exactly 2 sides of equal lengths.

What are identities trigonometry?

Identities are "equations" that are always true.

For example, the equation sin(x) = cos(x) is true for x = pi/4 + kpi radians where k is any integer [ = 45 + 180k degrees], but for any other value of x the equation is not true.

By contrast, the equation sin2(x) + cos2(x) = 1 is true whatever the value of x. This is an identity.

If a right circular cylinder with radius 7 Cm contains 1077 cm cubed of water a rock is measured in the water and the level rises 3 cm what is the volume of the rock?

First obtain the height of the cylinder.

Height = 1077/area of the base

(i.e H = 1077 divided by pie-radius-squared)

Next get how much water does 1cm of height contain.

Take 1077/height.

Therefore, volume of rock = 1cm height's volume x 3

How do you solve for y square root of 2 x minus 1?

Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared", "cubed" etc. Please use "brackets" (or parentheses) because it is impossible to work out whether x plus y squared is x + y2 of (x + y) 2.

Here, it is not clear whether the question is about y = sqrt(2x - 1) or y = sqrt(2x) - 1. The solutions in the two cases are different.

What is the third side of a triangle and its other angles that has two sides of 7.59 cm and 5.67 cm with an included angle of 72.23 degrees between them?

Let the angles be A B C and their opposite sides be a b c and by using trigonometry in the form of the cosine rule the 3rd side works out as 7.97 cm and the other angles are 42.65 degrees and 65.12 degrees.

How do plumbers use trig?

A key part of plumbing is installing piping with the proper slopes for drainage. That requires a good understanding of angles and triangles.

Where does the word fight come from?

it comes from an Old English word 'Lyftgelac' meaning flight through the air. The word 'to flee' in Old English is 'Aetfleon'

How do you draw the Arctic Circle?

The Arctic Circle is an imaginary line on globes and charts at about 66.5°N latitude. Locations north of the Arctic Circle can experience at least one 24-hour period of "night" during the winter. At the North Pole, this becomes 6 months of daylight and 6 months of night.

To "draw" the Arctic Circle, make a circle centered on the North Pole, about 2600 kilometers (1616 miles) in radius.

How do you use a ladder?

Click the link below for a video on the proper use of ladders.

How do you make a model for maths?

be more precise. what in maths. area or length or like pi or something. make it with clay its the easiest or make a diagram with paper.