Trigonometry

the conditions for congruent figures is that they have same shape and size,they have to be coincide each other. answer by mohit kumar pal

- (sq rt 2)/2 approx. -0.7071

just an angle, like any other angle.

1160

cosine 45° = √2/2 (Square root of 2 over 2)

di baya mao

Trigonometric ratios are characteristics of angles, not of lengths. And, by definition, the corresponding angles an similar triangles have the same measures.

Since the hypotenuse (denominator) is always greater than the opposite or adjacent side (numerator), the ratio will always be smaller than one.

sinh(x) = 0.5*(ex - e-x) where x is measured in radians.

Suppose csc(x)*sin(x) = cos(x)*cot(x) + y

then, ince csc(x) = 1/sin(x), and cot(x) = cos(x)/sin(x),

1 = cos(x)*cos(x)/sin(x) + y

so y = 1 - cos2(x)/sin(x) = 1 - [1 - sin2(x)]/sin(x) = [sin2(x) + sin(x) - 1]/sin(x)

3

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.

90 degrees is one

0.5735764264 (nearest 10 decimal places).

No. It can be used on any triangle.

They do not. They are not animate nor sentient and so they are incapable of communicating.

Cosecant(115 deg) = 1/sine(115 deg) = 1/0.9063 = 1.1034

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

The cosine function on a right triangle is Adjacent leg divided by the hypotenuse of the triangle.

with a sine wave

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.

General answer: Math

Specific Answer: Taylor Series

Sine, cosine, and tangent all assume you have a right triangle (where one angle is 90 degrees). Each function operates on one number, which represents another angle (call it x) in the triangle. We write these functions as sin(x), cos(x), and tan(x).

Now, we're going to give names to each of the 3 sides. The longest side (the one not touching the right angle) is the hypotenuse. The side touching our angle x, but not the hypotenuse, is the adjacent side. The left-over side is the only one not touching our angle x, which we call the opposite side. We call the length of the hypotenuse h, the length of the adjacent side a, and the length of the opposite side o.

Then sin(x)=o/h

cos(x)=a/h

tan(x)=o/a.

People use the made-up word "sohcahtoa" ("SOAK-a-TOE-ah") to remember this. each third of the word stands for a different function: the letters "soh" stand for "sine" is "opposite" over "hypotenuse", and similarly for "cah" and "toa".

They are co-functions meaning that 90 - sec x = csc x.