Trigonometry

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.

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).

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.

Basically, it IS a curve.

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.

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.

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).

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

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.

cos(270) = 0

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° .

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

By using the sine ratio, you know two sides of the right triangle (the opposite and hypotenuse) and so can work out the third side (adjacent) using Pythagoras (opposite2 + adjacent2 = hypotenuse2).

You can then use the trigonometric ratios to calculate cos θ, sec θ, cot θ, and the hypotenuse you already have.

Sin θ = opposite/hypotenuse = 2/x

⇒ opposite = 2, hypotenuse = x, and adjacent = √(x2 - 4)

Thus:

cos θ = adjacent/hypotenuse = √(x2 - 4)/x

sec θ = 1/cos θ = hypotenuse/adjacent = x/√(x2 - 4)

cot θ = 1/tan θ = adjacent/opposite = √(x2 - 4)/2

Hypotenuse = x.

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.

You can rationalize the denominator by multiplying this fraction by a fractional form of one in radical form.

3/sqrt(2) * sqrt(2)/sqrt(2)

= 3sqrt(2)/2

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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.

Positive or negative 4i

Say you want a bridge 400 m long. It will consist of 400 1 meter upside down triangles. Wait...it's a triangle, therefore you need to know how much material the other sides are! Well, worry know more, there are trig functions on calculators!