Trigonometry

Volume of pyramid = 1/3 Base x Height

100 = 25h/3

25h = 300

height = 12cm

cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25)

Note: cos(a)=cos(-a) for any angle 'a'.

cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.

The answer is given below:

cos(a)cos(b)-sin(a)sin(b)=cos(a+b)

a=7pi/12 and b=pi/6

a+b = 7pi/12 + pi/6 = 7pi/12 + 2pi/12 = 9pi/12

We want to find cos(9pi/12)

cos(9pi/12) = cos(3pi/4)

cos(3pi/4)= cos(pi-pi/4)

cos(pi)cos(pi/4)-sin(pi)sin(pi/4)

cos(pi)=-1

sin(pi)=0

cos(pi/4) = √2/2

sin(pi/4) =√2/2

cos(pi)cos(pi/4)-sin(pi)sin(pi/4) = - cos(pi/4) = -√2/2

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

40 degrees

90 degrees is one

0.5735764264 (nearest 10 decimal places).

sin(t) = 2/3

sin2(t) + cos2(t) = 1

so cos(t) = ± sqrt[1 - sin2(t)]

but because t is in the first quadrant, cos(t) > 0 so cos(t) = + sqrt[1 - sin2(t)]

= sqrt[1 - 4/9] = sqrt[5/9] = sqrt(5)/3

Then sec(t) = 1/cos(t) = 1/sqrt(5)/3 = 3/sqrt(5) = 3*sqrt(5)/5

60

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.

Assuming the wall is vertical, the wall, the ground and the ladder form an isosceles right-angled triangle. Pythagoras tells us that the square of the length of the ladder, in this case 225 equals the sum of the squares of the other two lengths, ie the height where the ladder touches the wall and the bottom of the ladder's distance from the wall. As these distances are equal in an isosceles triangle each must be the square root of (225/2) ie sqrt 112.5 which is 10.6066, as near as makes no difference to 10 ft 71/4 inches

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.

In all there are [at least] 24 trigonometric functions and ratios. Half of these are circular and the other half are hyperbolic.

Sine and Cosine are basic trigonometric funtions, abbreviated as sin and cos.

Tangent is the third basic ratio defined as Sin/Cos.

For each of these three, there is a corresponding reciprocal function:

Sine -> Cosecant (cosec or csc)

Cosine -> Secant (sec)

Tangent -> Cotangent (cot).

Each of the above six has an inverse function, defined on an appropriate domain. They all are named by adding the prefix "arc", for example arcsin, which is usually written as sin-1.

The above are the circular functions. Each one of them has a corresponding hyperbolic equivalent. These are named by adding the suffix, "h", thus cosh, sech, arccosh [= cosh-1], etc.

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

To convert from radians to degrees, multiply by 180° and divide by pi.

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

This is a complicated subject, which can't be explained in a few words. Read the Wikipedia article on "eigenvalue"; or better yet, read a book on linear algebra. Briefly, and quoting from the Wikipedia, "The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain parallel to the original vector. For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector is scaled when multiplied by the matrix."

tan(65 radians) = 1.65, approx.