Trigonometry

The Internet was the result of some visionary thinking by people in the early 1960s who saw great potential value in allowing computers to share information on research and development in scientific and military fields. J.C.R. Licklider of MIT, first proposed a global network of computers in 1962. As more computers were added, multiple independent networks were created and that was the beginning of the internet. Constant research and technical improvements made the internet grow and develop into the world wide web as we know it today. The world web as used in common language (see, for instance, Merriam-Webster's definition) seems a good choice to describe this tool that is becoming more and more popular all over the planet. Just try and imagine for a few seconds the thousands of computers and the millions of wires inside and outside themthere must be in the entire planet. Can you get the picture? Must be similar to a really huge spiderweb. And then it is all so fine when your 'puter is running smoothly... and so frustrating when it freezes or breaks down that most of us feel lost or kinda caught in a trap of somekind. So again the word web seems a very good pick. Hope this helps!

It is an injective relation.

There are no hindrances. If you put your mind to it, any subject can be mastered.

If you know all three sides of a triangle, you can calculate the angles using the law of cosines. If you only want to know which angle is the smallest, it is much simpler: The angle that is opposite to the smallest side is the smallest angle; the angle that is opposite to the largest side is the largest angle.

sinx cscx = 1 is the same thing as sinx(1/sinx) = 1 which is the same as sinx/sinx = 1. This evaluates to 1=1, which is true.

The answer depends on what x is meant to represent. Without that information, the question is a waste of time.

Yes. Along with the tangent function, sine is an odd function. Cosine, however, is an even function.

It works out that each apple pie cost 16 and that each pumpkin pie cost 20

According to recent (August 2017) research by the University of New South Wales, it was an unknown mathematician (or mathematicians) in Babylon. They produced a tablet, known as Plimpton 322, which contains tables of trig ration. This was some 1500 years before the Greek astronomer Hipparchus who, until now, was regarded the father of trigonometry.

The answer will depend on what exactly x represents. With no information about that, the question is pointless.

The length of the hypotenuse would be approximately 24.41 and the angle, theta, would be approximately 35.

to give the basics for astronomy, distance calculation etc

Suppose the radius of a unit circle makes and angle, q, which is measured in an anti-clockwise direction from the positive horizontal direction (so that East = 0 degrees, North = 90 degrees and so on.

Consider the x and y coordinates of the point on the radius, at the circumference of the unit circle, as the angle of the radius changes.

It can easily be shown with a couple of very simple diagrams (which I cannot do on this browser!) that

x = sin(q) and y = cos(q).

That depends on the values of what but if you mean arithmetical operations then they are: addition, subtraction, division and multiplication

You use the Pythagorian Theorum, a2 + b2 = c2, where c is the length of the hypotenuse.

If a2 + b2 = c2 then a2 = c2 - b2.

Let's say that b is the side opposite Θ. Since sinΘ = b/c, a2 = 5 - 4 = 1, so a = 1.

Since tanΘ = b/a, tanΘ = 2.

Basically, it IS a curve.

If you use n terms from the Taylor expansion, the absolute value of the error is less than [|x|^(2n+1)]/(2n+1)!

If you use n terms from the Taylor expansion, the absolute value of the error is less than [|x|^(2n+1)]/(2n+1)!

If you use n terms from the Taylor expansion, the absolute value of the error is less than [|x|^(2n+1)]/(2n+1)!

If you use n terms from the Taylor expansion, the absolute value of the error is less than [|x|^(2n+1)]/(2n+1)!

There are many formulae in trigonometry, not just three. So the question cannot be answered without knowing which three you mean.

Tangent = sine/cosine provided that cosine is non-zero. When cosine is 0, then tangent is undefined.

A triangle is a flat area, therefore it has a surface area, not a volume. Density is unrelated to the problem; you would need some additional information to calculate the surface area.

To find unknown sides or angles of a triangle. For triangle ABC, if C is a right angle and you are using angle A the side a is the opposite of A, side b is the adjacent side of angle A and c is the hypotenuse.

Ex: Sin A = a/c, if you know any 2 you can solve for the 3rd.

Cos A = b/c, if you know any 2 you can solve for the 3rd.

Tan A = a/b, and again, if you know any 2 you can solve for the 3rd.

It's an equation that's sitting there begging us to find what values for Θ make it

a true statement.

For the first few moments, just to make it simpler to look at and to write, I'll

call cos(Θ) by the name 'C'.

You said that [ 2C2 - C = 1 ]

Subtract 1 from each side: [ 2C2 - C - 1 = 0 ]

This is a plain old quadratic equation.

When you factor it, it becomes . . . . . . (2C + 1) (C- 1) = 0

Setting each factor to zero in turn, you get the two roots:

C = 1

C = - 1/2

Now we can go back to the trig world:

cos(Θ) = C

cos(Θ) = 1 . . . . . Θ = any positive or negative multiple of 360° .

cos(Θ) = - 1/2 . . . Θ = (any positive or negative multiple of 360°) plus or minus 120° .

cos(270) = 0

A person who works in crystallography would know more. I have read that x-ray crystallography actually done by a woman whose name I forgot, was used to prove that DNA is a helix thru measurement of angles of diffraction of the x-rays.

'Trigonometry' comes from Greek: 'trigonon' = 'triangle' and 'metron' = 'measure'. So, basically, the measurement of triangles.