Trigonometry

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.

amplitude =7. to find the period, set 2x equal to 2∏. then x=∏=period

The two square roots of i are (k, k) and (-k, -k) where k = sqrt(2)/2 = 1/sqrt(2).

Used often in physics in finding vectors, such as current pull on a moving object. A ship going NE at so many knots while a cross current is going SE at so many knots. What would be the angle of travel sort of problem. Used all the time.

The absolute value of the sine function cannot exceed 1 and so sin(a) = 312 is not possible.

It is frequently used in mapping surveys.

For example, if you want to find the distance to a mountain peak, you would find the direction to that peak from two locations and measure the distance between those two locations. Triangulation based on trigonometry for the ASA triangle would enable you to work out the distance to the mountain peak without having to go there.

Yes, this is a perfectly legitimate thing to do in the trigonometric functions.

I will solve all your math problems. Check my profile for more info.