What is Cos: Definition and 318 Discussions

Cos Cob is a neighborhood and census-designated place in the town of Greenwich, Connecticut. It is located on the Connecticut shoreline in southern Fairfield County. It had a population of 6,770 at the 2010 census.Cos Cob is located on the western side of the mouth of the Mianus River. The American Impressionist Cos Cob Art Colony flourished in the late 19th and early 20th centuries. An offshoot of the group, the Greenwich Art Society, continues to support local artists in town.
The town of Greenwich is one political and taxing body, but consists of several distinct sections or neighborhoods, such as Banksville, Byram, Cos Cob, Glenville, Mianus, Old Greenwich, Riverside and Greenwich (sometimes referred to as central, or downtown, Greenwich). Of these neighborhoods, three (Cos Cob, Old Greenwich, and Riverside) have separate postal names and ZIP codes. From 1883 to 1885, the official post office name of Cos Cob was Bayport.
In 2015, Forbes ranked Cos Cob the 287th wealthiest place in the US with a median house sale price of $1,329,107.

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  1. L

    Vertical asymptote of cos graph?

    Homework Statement State one known vertical asymptote of the graph of 1/secx Homework Equations None The Attempt at a Solution 1/secx = cosx
  2. G

    Find the integral x^3 sqrt(x^2 + x^8 + 8) cos x dx

    Homework Statement Find the integral f(x) = x^3 sqrt(x^2 + x^8 + 8) cox(x) dx The Attempt at a Solution I need help starting. It appears to be either integration by parts and/or substituion.
  3. R

    Newton Applications. Help solving equation with sin and cos.

    Homework Statement At an airport, you pull a 18-kg suitcase across the floor with a strap that is at 45 degrees above the horizontal. Find the normal force and the tension on the strap, given that the suitcase moves with a constant speed and the coefficient of kinetic friction is 0.38...
  4. D

    Integrate sqrt((1-cos(x))/2) from 0 to 2π

    Erm, I have this integration question: sqrt((1-cos(x))/2) with an upper limit of 2pie and lower limit of 0. I can't seem to do it right. I tried simplifying it: sqrt((1-cos(x))/2) = ((1-cos(x))/2)^(1/2) = 1 - (cos^-2(x))^(1/2) = 1 - cos^-1(x) Then I intgrated 1... which becomes...
  5. Q

    Wave Equation: A = A cos (kx - ωt), Meaning & Significance

    a wave equation is given as A = A cos (kx - ωt) so why if someone describes the wave equation to be A = A sin (ωt - kx) , the argument of the sin function changes by a minus sign? and is there a meaning to it? also i still don't really understand why the minus sign in the first equation...
  6. F

    Proof of sen² 25º + cos² 45º + sen² 65º = 3/2

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  7. I

    Find y such that cos y=cos(90+y) and −90degrees <= y <= 0degrees?

    Homework Statement Find y such that cos y=cos(90+y) and −90degrees <= y <= 0degrees?Homework Equations cos(a+b)=sin(a)cos(b)+cos(a)sin(y)The Attempt at a Solution This is a question that came up in my linear algebra class. We just learned about dot product, but this doesn't seem like it's...
  8. J

    Solve sin cos: Find cos6x - 4cos4x + 8cos2x =?

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  9. Chewy0087

    Verifying Solution for cos^4 x in Terms of cos 4x & cos 2x

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  10. E

    Limit of cos x as x approaches 1 formal

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  11. P

    Solving the Wave Equation with D=A sin kx cos \omegat

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  12. Somefantastik

    Are these the correct cos and sin relations for the given values?

    if \mu = cos(\theta) and \mu_{0} = cos(\theta_{0}) and cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi) Then cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi) Is this not correct?
  13. S

    Why Is Cosine Used to Calculate Induced Voltage in a Conductor?

    http://www.berkeleyscience.com/maxwells.htm """""When a conductor (a wire) is placed in an electric field, the field may induce a voltage in the conductor. The diagram shows an electric field in the x direction with magnitude E. If the conductor is perpendicular to the E field, there is no...
  14. J

    Can I get the integral of cos( t^2/2)?

    Can I get the integral of cos( t^2/2)?
  15. I

    Proving sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec

    ok ... here's my problem i need to prove that the LHS = RHS sin^2 + 2cos - 1 / 2 + cos - cos^2 = 1 / 1 + sec i tried to use the pythagarean identies and substitute the 1 and 2 but tht isn't getting me anywhere .. please help
  16. N

    Finding the Number of Solutions in [0,2pi) for log5(cos x) = -1/2

    Homework Statement -log5(cos(x)) = -1/2 How many answers are there in the interval [0,2pi) The Attempt at a Solution 5^-1/2 = cos(x) 1/sq rt 5 = cos(x) sq rt 5/5 = cos(x) 0.447 = cos(x) x = 63.43 Basically, I have no clue how to find the number of answers in the interval ; ( I...
  17. X

    I (t ) =15 2 cos (2π 60t ) [A]

    A wire has a current given by i (t ) =15 2 cos (2π 60t ) [A]. Determine how many electrons cross a particular point on the wire, moving from right to left, in the time interval 0 < t < 0.001I don't get this one. What equation do Ineed to use? I can't find the right one, but it seems so easy...
  18. D

    How to integrate cos( sin(x) ) from 0 to pi

    Homework Statement \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x The Attempt at a Solution If I use u = \pi-x I get : \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x = \int_{0}^{\pi} \sin ( \cos x ) \mbox{d}x but then what?
  19. O

    Plotting g = 3 cos (10pi t) Convolved with 4 Impulse (t +0.1) in Matlab

    Homework Statement plot using matlab: g = 3 cos (10pi t) convolved with 4 impulse (t +0.1) Homework Equations The Attempt at a Solution x = -10:0.1:10; u = 3*cos (10*pi*x); v = 4*dirac(x + 1./10); y = conv (u,v); plot (x,y); but i keep getting this error: Error using ==>...
  20. B

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    Homework Statement i have to create a mathematical forumal from data of high and low tide depths and times. from that predict the next weeks outcome. it has to have sin or cos in the equation. a*COS (bx+c)+d or sin. this is the data given Mon 09/03/2009 Tue 10/03/2009 Wed 11/03/2009...
  21. N

    Solving an equation involving sin and cos terms

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  22. C

    Simple harmonic motion: why cant you divide by cos?

    The displacement, x= Acos(\varpit+\phi), repeats for every increase in 2pi. Why can't I make the above equal to Acos(\varpit+\phi + 2pi), and divide by cos. This gives \phi]=0. This is clearly wrong. Why? And how does angular frequency apply to a mass on a spring anyways, it doesn't move in a...
  23. X

    Is Using Exponent Identities Allowed in Solving Trigonometric Integrals?

    Homework Statement Compute \int^{\pi/2}_{0} \frac{sin^{2009}x}{sin^{2009}x + cos^{2009}x} I used the identity cos^{2}= 1 - sin^{2}, but instead I set the exponent as 2009. And so I ended up with the answer being -1. I'm just wondering whether this is a legal solution or am I not allowed to...
  24. T

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  25. K

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  26. R

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  27. A

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  28. K

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    Homework Statement how could i prove that cos x= sum (n=1 to 00) [((-1)^n) * x^(2n)/((2n)!)] is continuous and differentiable at each x in R Homework Equations the Taylor Expansion of cosine is the given equation The Attempt at a Solution basically i need to prove that the...
  29. icystrike

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  30. R

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    Homework Statement I can not determine the solution to the diff. eq. Homework Equations \ddot{x}+k \cos{x}=0. The constant k is postive. The Attempt at a Solution I tried solving it with the methods I know and it all ended up in a big mess. I am just not used to the second...
  31. G

    Deeper connection between exp() and cos()?

    Is there some mathematician who knows the "core reason" why exp() is connected with cos()? I mean I'm confident with "advanced maths for physicists", but maybe some abstract theory gives an answer to this. I was think of something like: |e^{i\phi}|=1 therefore it's a unit circle. But also...
  32. S

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    Homework Statement I have been given these two equations: x=2acos^2(x) , y = 2a(cos(x))(sin(x)) where a ranges from 0 to 5 and -2π < x < 2π I need to prove that these equations (when you plug in values for x) create points that when plotted, give you a circle with center (x-a) and radius a...
  33. T

    Adding sin plus cos with fractions containing square roots

    How do I solve: [sin (pi/3)] + [cos (pi/6)]? <--- "pi" is 3.14... I think that [sin (pi/3)]= (square root 3) divided by 2 AND that [cos (pi/6)]= (square root 3) divided by 2. Now I can't remember how to add fractions containing square roots. My textbook...
  34. F

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    f(x)=x4 cos(2/x6) g(x) <= f(x) <= h(x) how to get g(x) and h(x) by using the squeeze theorem?? I know is something like this -1 <= x <= 1 But how do i implement it here, and especially to the cos, sin, and tan??
  35. M

    How Do You Prove the Derivatives of Sin and Cos Functions?

    Hi. I believe this may have been addressed previously but I wanted to make sure since I don't think it was completed. Hi I know that differentiating sin = cos , and differentiating cos = -sin. Time to prove it. Q3: Prove that: \frac{d}{{dz}}\sin z = \cos z We know the McLaurin form...
  36. T

    Derivative of y = sin x * cos x

    I'm working through Kline's Calculus book, and am at the chapter on Integration on Differentiation of Trig Functions. A question asks to find the derivative of: (I've labeled all equations for easy reference) (1) y = sin x * cos x unlike the solution guide which advocates using the product...
  37. E

    Integral of Square of Reciprocal of √(a + cos t)

    [SOLVED] Integral of Square of Reciprocal of √(a + cos t) Homework Statement Demonstrate that \int_0^\pi \frac{dt}{(a + \cos t)^2} = \frac{a\pi}{(\sqrt{a^2 - 1})^3} where a > 0. The attempt at a solution I want to compute this using the Residue Theorem. The first thing I did was...
  38. D

    How Do You Integrate \(\sin 6x + 3\cos 5x\) Using Substitution?

    Homework Statement Integrate \int\sin 6x + 3\cos 5x dx Homework EquationsThe Attempt at a Solution The way I was taught was the 'u' substitution method. I know that \int\sin u du = -\cos u + C and I know that \int\cos u du = \sin u + C Here's what I've done so far \int\sin 6x + 3\cos 5x...
  39. X

    Prove that cos 20 is irrational

    I've started to work on the it, just tell me if I'm on the right track. cos (45-30) = (\sqrt{3} + 1) / 2\sqrt{2} so cos 15 is irrational. cos3x = 4cos^3x - 3cos x \Rightarrow cos 5 is irrational cos 4x... cos 20 If this is a bad way, maybe someone knows a better one. Here is what I think...
  40. E

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  41. D

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    [SOLVED] Trigonometry cos A + 1 My little sis needs help w/ the following problem for her homework and to tell you the truth, aside from the fact that I'm too busy I have no idea how to explain this to her step by step. I would appreciate an explanation on how to solve it -- a solution would...
  42. D

    Unravelling the Mystery of the 3 Forms of Double-Angle Formula for Cos 20

    How can there be three forms of the double-angle formula for cos 20?
  43. C

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    Im having an issue of when to use Cos and Sin. When calculating Force (Normal and Frictional) with multiple demension problems you are typically given the angle of the incline. When trying to calculate for Fgx (or basically x) I would think to use cos(theta) and when dealing with Fgy (or...
  44. G

    Limit of Product Cosine | Double-Angle Formulas for Sine | (0,π/2) Range

    Homework Statement Calculate for x\in(0,\pi/2) \lim_{N\rightarrow\infty}\prod_{n=0}^{N}cos(\frac{x}{2^{n}}) Hint: Use the Double-Angle Formulas for the sine. Homework Equations The Attempt at a Solution cos(x)\cdot cos(\frac{x}{2})\cdot cos(\frac{x}{4})\cdot... \frac{\sin2x}{2\cdot\sin...
  45. G

    Solving cos x = -x: What Does it Mean?

    This is only part of my question and I need the answer to continue, when does cos x = -x? on my calculator it is -.7390... isn't it supposed to be a nicer number ie pi over something?
  46. R

    Double integration with cos x^2

    ok so I have the problem ycos(x^2)dxdy with parameters dx=y^2 to 1 and dx=0 to 1 the first problem I have is integrating cos with respect to x^2. is it a double angle identity? the second is how do I go further if Y^2 gets added into the mix later? The attempts I have made have made me even...
  47. L

    Simple Trig Limit: Evaluate lim x->0 of (1-cos4x)/9x^2

    Homework Statement Evaluate the limits that exist: lim x->0 of \frac{1-cos4x}{9x^{2}} Homework Equations lim x->0 \frac{1-cosax}{ax} = 0 The Attempt at a Solution so far I've got this \frac{4x}{9x^{2}}\frac{1-cos4x}{4x} The second part has a limit of 0 but I don't know what to...
  48. R

    How to integrate tan x/ (1 - cos x) ?

    Im doing a differential equation and end up with my last step, which is an integration. I can't seem to remember how to integrate this one int. (tanx)/(1-cosx) hmmm [(sinx)/(cosx)] / (1-cosx) u = cosx du = -sinx dx throw a negative outside the integral...
  49. C

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    First off, thanks for your help. I feel like a dope because everything I'm doing looks correct to me, but my answer is not the same as the book or solution manual gives! I'm usually so good at finding my mistakes. Thanks for taking the time to help. Homework Statement...
  50. A

    Trigonometry sin and cos question

    My teacher told me that C sin(k x) + D cos(k x) = F sin(k x+gamma) if neither C nor D is 0 (gamma is a phase angle). How do you derive the expression on the right of the equal sign from that on the left?
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