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Topic: Cos

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In the News (Fri 14 Jun 19)

 DCB - Online Information article about DCB
equation equals sin B sin C+cos a (cos A - sin B sin C cos a) =sin B sin C sin' a+cos a cos A, and this is equal to sin b sin c + cos A (cos a—sin b sin t cos A) or sin b sin c + cos cos a cos A..
cos RA +B) cos la cos b sin C = cos c cos l (A +B — C) sin la sin b sin C = cos c cos 1(A +B +C) These formulae were given by Schmiesser in Crelle's Journ., vol.
If we use the values of sin la, sin 1b, sin lc, cos la, cos lb, cos lc, given by (9), (Io) and the analogous formulae obtained by interchanging the letters we obtain by multiplication Schmelsser's sin la cos b sin C=sin lc cos 1(B+C—A) Formulae. /DAH_DEM/DCB.html   (1428 words)

 UCSD Math Club - Fun & Games
The derivative of P with respect to A is dP/dA (A, B) = cos B (sin A cos (Pi - A - B) - cos A sin (Pi - A - B)).
Concluding: the maximum over all A and B of cos A cos B cos C where C = Pi - A - B is 1/8 so cos A cos B cos C is less than or equals to 1/8.
One can also prove the above result without calculus by transforming the expression 1 - 8*cos A cos B cos C into a sum of squares by using trig functions. /~mathclub/games/brainteaser-archive/cos.html   (409 words)

 math lessons - Sum and difference formula (trigonometry)
sin(a + b) = cos(90 - (a + b)) = cos((90 - a) - b) = cos(90 -a)cos b + sin(90 - a)sin b = sin a cos b + cos a sin b
cos(a + (-b)) = cos a cos (-b) - sin a sin (-b) = cos a cos b - sin a (-sin b) = cos a cos b + sin a sin b
sin(a + (-b)) = sin a cos (-b) + cos a sin (-b) = sin a cos b + cos a (-sin b) = sin a cos b - cos a sin b /lessons/Sum_and_difference_formula_(trigonometry)   (327 words)

 PHYS424 Exam 2
Consider a particle of mass m that is free to move in a one-dimensional region of length L that closes on itself (for instance, a bead which slides frictionlessly on a circular wire of circumference L.
(b) Using the results of part (a), find the energy and wavefunction for the lowest state(s) in the three-dimensional harmonic oscillator with an angular momentum whose magnitude is h-bar (l=1).
(b) Without solving for the radial dependence find the best minimum value you can for the number of states degenerate with (having the same energy as) each one of these states. /mvb/PHYS424htm/exam3f02.html   (696 words)

Barycentrics sin A (cos B - cos C) : sin B (cos C - cos A) : sin C(cos A - cos B) = a(b - c)(b + c - a) : b(c - a)(c + a - b) : c(a - b)(a + b - c)
Trilinears 1/(cos B - cos C) : 1/(cos C - cos A) : 1/(cos A - cos B) = 1/[(b - c)(b + c - a)] : 1/[(c - a)(c + a - b)] : 1[(a - b)(a + b - c)]
Barycentrics (sin A)/(cos B - cos C) : (sin B)/(cos C - cos A) : (sin C)/(cos A - cos B) = a/[(b - c)(b + c - a)] : b/[(c - a)(c + a - b)] : c/[(a - b)(a + b - c)] /ck6/encyclopedia/part4.html   (7727 words)

Law of Cosines: a) cos a = cos b cos c + sin b sin c cos A where two sides and the included angle were known b) cos A = - cos B cos C + sin B sin C cos a where two angles and the included side were known 2.
cos 161.69 D = 61.83 lat centroid = 9O - D = 28.17 sin N sin 161.69 ------------ = ------------- sin 37.38 sin D sin N = sin 161.69.
cos D) cos C = --------------------------------- cos C cos lat A. /~jwg9/dymaxion/appendix.htm   (697 words)

 Nick's Mathematical Puzzles: Solution 119
Rearranging, we have sin A (sin A - cos B) = sin B (cos A - sin B).
Suppose both factors are positive, in which case sin A > cos B > 0 and cos A > sin B > 0.
Similarly, if we suppose both factors are negative, in which case 0 < sin A < cos B and 0 < cos A < sin B, we arrive at 1 < 1; again a contradiction. /puzzles/p119s.html   (254 words)

 Trigonometric identity - Wikipedia, the free encyclopedia
The following notations hold for all six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
If (a, b, c) are the lengths of the sides of a right triangle, then (a
is negative, take its opposite and use the supplement of B. /wiki/Sum_and_difference_formula_(trigonometry)   (1295 words)

 Law of Cosines
The trick is to write the law of cosines as a quadratic in terms of the unknown side.
In triangle ABC, b = 4, c = 5 and the measure of angle A is 51°.
B > 0, then there are two solutions (b > a sinB) until b > a, at which point there is a single solution. /~rweeks/trig/law_of_cosines.htm   (316 words)

Unfortunately, cos B is the ratio of the two sides you don't know, namely, a/c.
Therefore the cosine of B equals the sine of A.
The cosine of A relates b to the hypotenuse c, so you can first compute c. /~djoyce/java/trig/cosines.html   (526 words)

LAW OF SINES and LAW OF COSINES Let the lengths of the three sides of a triangle be denoted a, b, and c.
Let the angle opposite side a be u, and the angle opposite side b be v and the angle opposite side c be w.
It is important to use radians whenever derivatives are involved, because otherwise the familiar formulas for derivatives of trigonometric functions are not valid. /faculty/matchett/trig.txt   (457 words)

 Multiple Angle Identities
Since cos (A + B) = cos A cos B - sin A sin B, it follows that
Since sin (A + B) = sin A cos B + cos A sin B, it follows that
Given that x / 2 is in quadrant II and cos x = 1 / 2, find cos (x / 2) and sin (x / 2). /precal/part5/part5.4.html   (384 words)

 IBM Research Ponder This March 2001 Solution
V^2 = D g / (2 sqrt(2) * (cos B) * (sin B + cos B)).
Its horizontal velocity is then (v cos b).
Letting (g) be the acceleration due to gravity, we see that after time (t = 2 v sin b / g) the vertical velocity will have changed from (v sin b) to (- v sin b), and the ball will have returned to its initial vertical position. /Comm/wwwr_ponder.nsf/solutions/March2001.html   (294 words)

 An Introduction to FM
cos A cos B = 1/2 (cos (A - B) + cos (A + B)) sin A sin B = 1/2 (cos (A - B) - cos (A + B))
Since cos takes an angle as its argument, f(t) "modulates" (that is, changes) the angle passed to the cosine.
If we have a spectrum B made up entirely of sines (or entirely cosines), we can then multiply it by sin A (or cos A) then add the two resulting spectra, and the (A + B) parts cancel. /software/snd/snd/fm.html   (3815 words)

B = arcsin((cos(A) * R - 1) / R) - A + (4X - 1) * PI / 2
B = -arcsin((cos(A) * R - 1) / R) - A + (4X + 1) * PI / 2
It is a formula designed to pinpoint the distance required to move from one horizontal pixel to another (integer incrementation) as theta traverses the edge of a circle or ellipse. /news/geeknews/2002mar/gee20020314010738_comments.dat   (1970 words)

 Quantum Mechanics
Carrying out a "measurement" of an observable B on a system in a state A> has the effect of collapsing the system into a B-eigenstate corresponding to the eigenvalue observed.
Different operators can have different eigenvectors, but the eigenvector/operator relation depends only on the operator and vectors in question, and not on the particular basis in which they are expressed; the eigenvector/operator relation is, that is to say, invariant under change of basis.
Graduate students in physics spend long years gaining familiarity with the nooks and crannies of Hilbert space, locating familiar landmarks, treading its beaten paths, learning where secret passages and dead ends lie, and developing a sense of the overall lay of the land. /entries/qm   (3833 words)

projecting onto plane containing stave face perpendicular, note that: tan(a) / tan(a') = cos(b) where: a = 180/n a'= the projected angle b = the slant of the stave face so: tan(a') = tan(180/n) / cos(b) 3.
divide thru by cos^2 tan^2 + 1 = 1 / (cos^2) cos = 1 / (1 + tan^2)^.5 we get: cos(c) = 1 / (1 + ((w2 - w1) / 2 * h) ^2)^.5 6.
b is the angle of the conical shell's edge. /kseifert/misc/bongo.txt   (360 words)

 LAMBDA - Coordinate Projections Used for IRAS Maps
The orthographic projection, like the gnomonic projection, is a projection of the celestial sphere onto a tangent plane, but the center of projection is infinitely distant from the tangent plane.
The Lambert normal equivalent cylindrical projection was used to provide an equal area projection of the sky within 10° of the Galactic plan for the Galactic Plane Maps.
NOTE: The arctangent functions for B and alpha must be four-quadrant arctangents. /product/iras/coordproj.cfm   (1018 words)

I want to find a solution for the angles a, b, c, d such that the derivative with respect to time of either angle b or d is maximized when I substitute the sines, cosines, and derivatives of the four angles into q'.
Assuming you manage to get a solution (which gives the cosines of a, c, and d in terms of the cosine of b), differentiate the right side of the first equation and substitute out all sines and the cosines of a, c and d (leaving cos(b)).
I'm using the sine and cosine of a and c as amplitudes, which is why I needed them between 0 and pi / 2.0 inclusive. /~rusin/known-math/95/DE_on_s3   (1959 words)

 2.3 Properties of Trigonometric Functions
= cos a cos b — sin a sin b + i(cos a sin b + cos b sin a)
exp i(a+b) = cos (a + b) + i sin(a + b) = (exp ia) * (exp ib)
And we have cos 0 = 1, sin 0 = 0. /ans7870/18/18.013a/textbook/HTML/chapter02/section03.html   (491 words)

 Physics and Astronomy Forums - I need help with these problems
([sin b + cos 2b -1] / [cos b - sin 2 b]) = tan b
3 sin b - 4 (sin ^3) b - sin b = 2sin b cos 2b
2 sin b - 3 sin b + sin 3b= 2sin b cos 2b /community/forums/printthread.cfm?Forum=9&Topic=1510   (1178 words)

 KryssTal : Trigonometry
- (2 × a × c × Cos B) c
B = 180 - A - C = 180 - 32 - 45.5
Area = (a × b × Sin C) / 2 = (a × c × Sin B) / 2 = (b × c × Sin A) / 2 /trigonometry.html   (1111 words)

The coratios are the ratios of complementary angles (angles whose sum is 90 deg); for example, cos A = sin (90 deg - A).
For example, cos (180 deg + A) = -cos A, where A is an acute angle.
The sine formula (sine rule), which applies to any triangle ABC with sides a, b, and c, is a/sin A = b/sin B = c/sin C = 2R where R is the radius of the circumscribing circle. /mat112dir/trig.html   (1095 words)

 7.8 Math 10 Pure - Measurement
Solve the triangle with sides a = 3, b = 5, c = 7.
Since we could have just as well done this with the letters switched around any way we wanted, we can write it in three different ways.
let a = 120, b = 170, c = 220. /lburns/measurement_7.8.html   (317 words)

 Biola University Academics
Thus the trilinear coords of P are cos
C'AB, where A', B', C' are the centers of the circumcircles of triangles PBC, PCA, PAB respectively.
These 7 arcs, together with other 7 arcs from C to A, and another 7 arcs from A to B form a mesh so that each of the points H,Y,F,I,D,W,O is a point of concurrency of 3 arcs out of the 21. /~woopy/math/hyfidwo.htm   (594 words)

The net effect is that (using the substitution a= x/cos(b)) you'll still trace out the same lines as before, but the different values of a that will be used will be fewer when cos(b) is smaller.
Once you've picked b, the set of points you'll get by choosing different a's will trace out a circle of radius cos(b).
As b approaches pi/2 (90 degrees), your > many choices of a will give you lines very close together, and in fact at > b=pi/2 all choices of a give the same line. /~rusin/known-math/95/grassmans   (2274 words)

 Math 112                      Lab 3
a and c on the graphs of y = a sin (x – c) or y = a cos (x – c).
a on the graph of y = a sin x or y = a cos x.
b x) for different combinations of values of /math/activities/math_112_advanced_graphs.htm   (307 words)

 Right Triangles
Note that cotangents are tangents of complementary angles, which means that cot A = tan B, and cosecants are secants of complementary angles, and that means that csc A = sec B.
Note: as usual, in all exercises on right triangles c stands for the hypotenuse, a and b for the perpendicular sides, and A and B for the angles opposite to a and b respectively.
As a balloon passes between two points A and B, 2 miles apart, the angles of elevation of the balloon at these points are 27° 19' and 41° 45', respectively. /~djoyce/java/trig/right.html   (2174 words)

 Philetas of Cos - Wikipedia, the free encyclopedia
Philetas of Cos, Alexandrian poet and critic, flourished in the second half of the 4th century BC.
Philetas was also the author of a vocabulary called "Aro/cra, explaining the meanings of rare and obscure words, including words peculiar to certain dialects; and of notes on Homer, severely criticized by Aristarchus.
He is frequently mentioned by Ovid and Propertius, the latter of whom imitated him and preferred him to his rival Callimachus, whose superior mythological lore was more to the taste of the Alexandrian critics. /wiki/Philetas_of_Cos   (231 words)

 Hippocrates - Wikipedia, the free encyclopedia
Hippocrates recommended that physicians record their findings and their medicinal methods, so that these records may be passed down and employed by other physicians.
Other Hippocratic writings associated personality traits with the relative abundance of the four humours in the body: phlegm, yellow bile, black bile, and blood, and was a major influence on Galen and later on medieval medicine.
They are actually a group of texts written by several different people holding several different viewpoints erroneously grouped under the name of Hippocrates, perhaps at the Library of Alexandria. /wiki/Hippocrates   (231 words)

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