Trigonometry

with a sine wave

A function cannot be one to many.

Suppose y = tan(x)

Now, since tan(x) = tan(x + pi)

then tan(x + pi) = y

But that means arctan(y) can be x or x+pi

In order to prevent that sort of indeterminacy, the arctan function must be restricted to an interval of width pi.

Any interval of that width would do and it could have been restricted to the first and second quadrants, or even from -pi/4 to 3*pi/4. The problem there is that in the middle of that interval the tan function becomes infinite which means that arctan would have a discontinuity in the middle of its domain. A better option, then, is to restrict it to the first and fourth quarters. Then the asymptotic values occur at the ends of the domain, which leaves the function continuous within the whole of the open interval.

If r-squared = theta then r = ±sqrt(theta)

It means the ratio of the opposite angle to the hypotenuse of a triangle for angle "x". This is for a right triangle.

-16t2 + 64t + 1224 = 0

Multiply both sides by -1

16t2 - 64t - 1224 = 0

Divide both side by 8

2t2 - 8t - 153 = 0

Cannot be factored so use the formula (-b (+ or -)(root of b2 - 4ac)) / 2a

sinθ = O/H

cosθ = A/H

tanθ = O/A

cosθ*tanθ = A/H * O/A = AO/AH = O/H

Therefore, sinθ = cosθtanθ = O/H

(Notes: O=opposite, A=adjacent, H=hypotenuse)

Cos(120) = -0.5

tan(20 deg) = 0.3640 approx.

You seem not to be aware but you could have obtained the answer much more easily and quickly by using the calculator that comes as part of your computer.

Yes, that is why they are called "principal". The domains are restricted so that the functions become injective.

Mensuration is often based on making use of a model or base object that serves as the standard for making the calculations. From that point, advanced mathematics is employed to project measurements of length, width, and weight associated with like items. The end result is data that can help to make the best use of resources available today while still planning responsibly for the future.

While mensuration is normally associated with measurements within the timber industry, the general principles can be applied in other venues as well. For example, the basics of mensuration can be used to project any type of phenomenon where growth of some sort is anticipated. Thus, mensuration may be used to project learning curves, the process of managing any type of renewable resource, or even something as simple as a projected average growth pattern for an individual.

In general, the utilization of the principles of algebra and geometry in the measuring process are capable of providing reliable data that is based on the existence of a specified set of factors. However, it is important to note that mensuration is not the only approach that is used to project future growth and volume. Because there is always the chance for unexpected elements to enter the process, the measurements obtained from the process of mensuration are normally considered a baseline. Predictions of future patterns that do factor in acts of nature and other volatile factors are then created using the results of the mensuration process as the foundation rather than the sole projection of the ultimate outcome.

2 sin^2 theta = 1/4

sin^2 theta = 1/8

sin theta = sqrt(1/8)

theta = arcsin(sqrt(1/8))

There is no way to find perimeter from a 3D figure. However, you can find the perimeter of a side of a triangular prism by using perimeter formulas for a parallelogram or triangle.

Periodically

The answer depends on whether a or c is the hypotenuse: b cannot be the hypotenuse since the hypotenuse MUST be the longest side.

Suppose a is the hypotenuse.

Then a2 = b2 + c2 = 122 + 182 = 144 + 324 = 468. So a = 21.63 inches (approx).

Suppose c is the hypotenuse.

Then c2 = b2 + a2 = 182 = 122 + a2. So a2 = 180 and a = 13.42 inches (approx).

Cotangent is 1 / tangent.

Since tangent is sine / cosine, cotangent is cosine / sine.

Inverse sine is defined for the domain [-1, 1]. Since 833 is way outside this domain, the value is not defined.

In Geometry, you learn about triangles. In Trigonometry you learn even more about triangles.

-1273 degrees lies in quadrant two. Simply add 360 degrees repeatedly until it becomes positive, giving 167 degrees. Note that is greater than 90 and less than 180, making it quadrant two.

A useful property in Trigonometry is:

tan(x) = sin(x) / cos(x)

So, cos(x) tan(x) = cos(x) [ sin(x) / cos (x)]

= sin(x)

cos(195) = -0.965925826289

sin-1 (0.91) = about 1.14328 radians.

If you have the sine of an angle and you need to find the angle, you have a

few choices. They're exactly the same choices that you have if you're going

the other way ... you have the angle and you need to find its sine:

-- pocket calculator, or computer . . . the way it's most often done these days

-- look it up in a table in a reference book

-- calculate it on paper from an infinite series . . . technically possible, but no reason

to subject yourself to the heartburn unless you need extreme precision, better than

what you can get with a 10-digit calculator.

26 = 64

There are 2 cups in a pint. There are 2 pints in a quart. There are 4 pints in a half gallon, like if you bought a half a gallon if milk at a store. There are 8 pints in a gallon.

10 pints equals 20 cups.

10 pints equals 5 quarts

10 pints equals 2 and a half gallons.

10 pints equals 1 and a quarter gallons.

Hope I helped!