Trigonometry

cos20 x cos40 x cos80 = 0.0300 radians

= 0.125 degrees

(the value for radians is given to four decimal places, the value in degrees is exact)

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

sine 40° = 0.642788

just an angle, like any other angle.

1160

If tan(theta) = x

then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x

= sqrt(1 + 1/x2)

Tan 42 degrees = 0.9004

tan(135) = -tan(180-135) = -tan(45) = -1

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

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

General answer: Math

Specific Answer: Taylor Series

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

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.

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.

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.

Permutations of 10 letters taken 3 a time = 10 x 9 x 8 = 720

1/cos

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.