What is Sin: Definition and 451 Discussions

In a religious context, sin is a transgression against divine law. Each culture has its own interpretation of what it means to commit a sin. While sins are generally considered actions, any thought, word, or act considered immoral, selfish, shameful, harmful, or alienating might be termed "sinful".

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  1. P

    Eigenfunction is made entirely of sin functions

    Homework Statement The text claims that any function can be constructed from eigenfunctions. BUt if the eigenfunction is made entirely of sin functions than it cannot construct even functions? So it cannot construct any function? That is why the Fourier series has both sin and cos functions.
  2. L

    The Taylor series expansion for sin about z_0 = (pi/2)

    Homework Statement Expand cos z into a Taylor series about the point z_0 = (pi)/2 With the aid of the identity cos(z) = -sin(z - pi/2) Homework Equations Taylor series expansion for sin sinu = \sum^{infty}_{n=0} (-1)^n * \frac{u^{2n+1}}{(2n+1)!} and the identity as given...
  3. A

    How can I integrate x^3 sin x without using integration by parts?

    I'm trying to integtrate x^3 sin x without using integration by parts. I have set up the equation to either: int x^3 cosx dx = (Ax^3 + Bx^2+Cx+D)cos x + K or int x^3 coxs dx = (Ax^3+Bx)sinx + (Cx^2+D)cosx +K but I'm having trouble... any help would be appreciated!
  4. T

    Exploring the Sequence of Transformations for Mapping y = sinx to y = 3sin2x

    Describe fully the sequence of two transformations that maps the graph y = sinx onto the graph of y = 3sin2x Well I know that when x = 45 y = 3, when x = 90 y = 0 when x = 135 y = -3 and so on, but tranformations and translation (move), reflection, rotation and englargment. I would presume...
  5. S

    Solving Summation of sin with n^2 - Svensl

    Hello, Can anyone give some hints on how to solve this: \sum_{n=0}^{K-1}\frac{sin(2\pi n^2\Delta)}{n} It's just the n^2 that complicates things. I tried re-writing it as Im\sum_{n=0}^{K-1}\frac{e^{j n^2 x}}{n}, where x=2\pi \Delta but I cannot solve this either. Thanks, svensl
  6. R

    Does cos + sin always equal 0?

    does cos + sin = 0?
  7. U

    Prove torque equation 2sin^2(theta/2) * cos(theta + beta) = sin (beta)

    Homework Statement A uniform smooth plank weight W and length 2a is hinged to the bottom horizontal edge of a smooth, fixed plane inclined at angle (beta) to the horizontal. A sphere of radius (1/2)a and weight 2W is placed between the plank and the plane. Assume no friction. Prove that, in...
  8. B

    Find Critical Numbers of sin^2 x + cos x Function

    Homework Statement Find any critical numbers of the function Homework Equations sin^2 x + cos x The Attempt at a Solution I actually have a sort of silly question. Woud sin^2 in the equation be solved using the differeniation rule of d/dx[sin x] = cos x or d/dx [sin u] = (cos...
  9. J

    Comparing Maclaurin Series of cos x and sin x

    I have been asked to differentiate cos x and six...the maclaurin series versions... I have done the general and specific terms as shown below. Im not sure if these are correct? thanks General Terms cos x = ∑ (-1)n (x^(2n) / (2n)!) COS x = ∑ (-1)n (x^(2n+1)/ (2n +1) / (2n)!)...
  10. E

    Solving a Diff. Eq. Involving Primitive of sen x^3

    Homework Statement I'm stuck trying to solve a differential equation at the point i need to calculate the primitive of sen x^3 Homework Equations The Attempt at a Solution I've thought on primitives by parts but I don't know how will I do it...
  11. G

    A series for sin az / sin pi z in complex analysis

    Homework Statement Show that \frac{\sin (az)}{\sin (\pi z)} = \frac{2}{\pi} \sum_{n=1}^{+\infty} (-1)^n \frac{n \sin (an)}{z^2 - n^2} for all a such that - \pi < a < \pi Homework Equations None really, we have similar expansions for \pi cot (\pi z) and \pi / \sin (\pi z) , this...
  12. R

    X=r(cos u+i sin u) and y=t(cos v + i sin v)

    I need help getting this one started... PLEASE... Given x=r(cos U + i sin u) and y =t(cos v + i sin v): Prove tha tthe modulus of (xy) is the product of their moduli and that the amplitude of (xy) is the sum of their amplitudes.
  13. S

    Solve Complex Sin Contest Question from 2003 | Exam Review Help

    Sin contest question from 2003-- Can't figure this question... it's exam review! help the questions is: A kid is 5m from a fence that is 4 m high. He throws a ball @ 45 degrees from the horizontal which just grazes the fence. How far beyond the fence does the ball land? You may assume that the...
  14. W

    What Are the Roots of sinh(z) = 1/2?

    Homework Statement Find all the roots of sin h(z) = 1/2 2. The attempt at a solution sin h(z) = [1/2](e^z - e^-z) = 1/2 => e^z -e^-z = 1 => e^2z - e^z - 1 = 0 {multiplied e^z bothsides} this is a quadratic equation in e^z using quadratic formula, e^z = [1+- sqrt(5)]/2 taking 'ln' on...
  15. T

    Solving a Power Series Question: X = yt/2(sinh yt + sin yt/cosh yt - cos yt)

    another power series question... I tried it for awhile but it just got out of hand and the amount of numbers got unbearable. Q. The increase in resistance of strip conductors due to eddy currents at power frequencies is given by : X = yt divided by 2 (sinh yt + sin yt divided by cosh yt -...
  16. D

    Exponential forms of cos and sin

    hi, my question is from Modern Engineering Mathematics by Glyn James pg 177 # 17a Using the exponential forms of cos(theta) and sin(theta) given in (3.11a, b), prove the following trigonometric identities: a) sin(x + y) = sin(x)cos(y) + cos(x)sin(y) and 3.11a is: cos(x) = 0.5*[ e^(jx)...
  17. S

    Why does sin converge not the cos?

    thanks......
  18. T

    Proving Sin 6x Cos 4x + Cos 4x sin 2x = Cos 2x tan 8x

    I am trying to prove this equation: Sin 6x Cos 4x + Cos 4x sin 2x = Cos 2x tan 8x Tan 8x does anyone have any idea??
  19. S

    Real life situation to a sin graph on position by time graph

    Here is the deal, no matter how many times you take the derivative of the sin graph, you never get zero b/c you get in a cycle, well, I just can't picture anything like that happening in real life b/c if you keep taking derivative, at some point of time, the graph has to be y=0 equation b/c the...
  20. M

    Double-Slit sin (2 theta) help?

    I'm in physics I and only in Trig for the first time this year (Jr in HS). I do not remember sin (2 theta) in any previous lessons. I need in help in the following problem using it. In a double-slit experiment with monochromatic light and a screen at a distance of 1.50 , the angle...
  21. K

    Conjugate of either sin or cos

    okay, so this particular equation involves me writing conjugate of either sin or cos, but hows that possible considering they both are real in the given problem? maybe i should convert sin and cos into their exponential form first? but then wt would be the conjugate of this...
  22. N

    Is tan: (-π/2, π/2) -> R a Homeomorphism?

    Show that tan: (-pie/2,pie/2)->R is a homeomorphism where tan = sin/cos To show that f and f^-1 are cts, it seems trivial from a sketch but how do you do it? For 1-1 tan(x) = tan(y) Need to knwo x =y tan(x) = sinx.cosx = siny/cosy = tany => sixcosy = sinycosx this gets you...
  23. M

    Help me understand x and y components, sin cos, etc.

    I'm really having difficulty understanding how to approach problems in my physics class due to 1. never having taken physics before, and 2. having a professor that I cannot understand (english is not his native language, and he speaks very soft/fast). We're now doing tension in class, and I'm...
  24. J

    Limits of a sin function: What is the limit as x approaches 0 of sin(1/x)?

    Consider the function f(x) = sin(1/x). (a) Find a sequence of x-values that approach 0 such that sin (1/x) = 0. [Hint: Use the fact that sin(pi) = sin(2pi) = sin(3pi) = ... = sin (npi) = 0.] (b) Find a sequence of x-values that approach 0 such that sin(1/x) = 1. [Hint: Use the fact...
  25. K

    Trigonometric Functionssimplify sin squared functions

    just looking at another question to do with trigonometric functions and I can't see how they simplify the follwing: 2sin^2x-3sinx-2=0 to (2sinx+1)(sinx-2)=0 again i prob thinking sumthin really stupid...but i can't see wat! cheers
  26. P

    How Does the Rule a Cos Theta + b Sin Theta Simplify Using Trigonometry?

    Hey, I’ve got a test in one week’s time and was studying through my textbook of geometry and trigonometry. I came across a “rule” which shows how to simplify expressions in the form of a \cos \theta + b \sin \theta but I do not understand how this “rule” works. The simplify rule: a \cos...
  27. I

    Finding an Integration Factor for (Cos(2y)-Sin (x)) dx-2 Tan (x) Sin (2y) dy = 0

    Hi there i am trying to make this equation look exact. (Cos(2y)-Sin (x)) dx-2 Tan (x) Sin (2y) dy = 0 What I've done so far is take the partial with respect to x and y. So, my M_{y} is equal to -2 Sin (2y)-0 and, my N_{x} is equal to -2(Sec^{2}(x)) Sin (2y) Which makes it...
  28. C

    Alternate angle for sin (2*theta) ?

    I believe this could be the easiest math post of the day, but it's been too long for me to recall. Anyways, I'm working on the problem where I have to find 2 alternate angles. I got the first (smaller) angle right which is sin(2*theta). Now I have to find the second (bigger) angle which is...
  29. H

    How to prove e^ix=cos x + i sin x

    How to prove e^ix=cos x + i sin x
  30. E

    How to Use Duality Property for Finding Fourier Transform of sin x / x?

    Hi, how do I find the Fourier transform of this function sin x / x, i.e., f* = Integral( sin x / x * exp( i*w*x) dx from -infinity to +infinity ). I've been using Jordan's Lemma up to this point, but it doesn't seem to apply here as a way to evaluate the integral. Thanks for any help.
  31. R

    Confused with quadrants with Cos Tan Sin

    Okay can anyone tell me why is this true for restriction of 0 < x < 360 sin(x)=0.15, x = 8.6 and 171.4 cos(x)=-.655 x = 130 and 230 tan(x)=0.75, x = 36.9 and 216.9 I don't see a pattern or rule... please co-ordinate me through the use of graphs if you can my teacher didn't explain it well.
  32. N

    How to Graph the Function P = 34730 + 200000 Sin x?

    My batteries of my calculator playing up I cannot draw the following graph: P= 34730 + 200 000 sin x Could someone please use a graph package to draw it and possibly attach it so I can have a look at it please :-) I need to view P against x. Thanks ever so much!
  33. N

    Confusion regarding sin and cos

    Generally I am confused about the use of sin and cos in physics problems. http://img188.imageshack.us/img188/3162/eg2gu.gif The torque about the beam's attachment to the wall is: T * 8 * sin(53) Where T is the tension of the wire. Why is sin the choice and not cos? The...
  34. J

    Help Solving for x: 246.25 sin x - 676.58 cos x = -27768.42

    Hello, could anyone help me calculate the value of x? 246.25 sin x - 676.58 cos x = -27768.42 Thank you.. James
  35. daniel_i_l

    Force and the Sin Wave - Exploring Average Force

    This is just something I was thinking about the other day: Lets say that we have an object with the mass of 1kg and at t=0: x=0m and v=0m/s. Now we apply a force over time t with the force: F=sin(t)N. that means that a=sin(t). To get v we integrate and get: v = 1-cos(t). Then we integrate...
  36. C

    Solving for a variable inside a sin()

    sin( degtorad( (180 - (180 - 360/x))/2 ) ) = y/z degtorad(degrees) means the the degrees inside the parenthesis are converted to radians. How do you solve for x? Thank you.
  37. D

    QM Problems with wavefunction given in sin and cos.

    Well, the question goes like this, A particle of mass m is trapped in an infinitely deep one-dimensional potential well between x = 0 and x = a and at a time t=0,, the wave fuction is given as Φ(x,t=0)=sin(((πx)/a))cos(((2πx)/a)) (i) What possible values may be found for energy of...
  38. N

    Why is sin (x+x) = sinx cosx + cosx sinx ?

    Why is sin (x+x) = sinx cosx + cosx sinx ? Simple explanation required please
  39. T

    What is the limit for cos (n pi) and sin (n pi)?

    may i know how to solve [ n^2 cos(n(pi)) ]/ n^2 + 42?? i have divided it by n^2 and get cos(n pi) / (42/n^2) and i can't solve already.pls help what is the limit for cos (n pi) and sin (n pi)??
  40. U

    Simplifying sin^2 2θ/(1+cos^2 2θ) as a Function of sin θ

    1. Express \frac{sin^2 2 \theta}{1+cos^2 2 \theta} as a function of sin \theta here's what I did: = \frac{4 sin^2 \theta cos^2 \theta}{1+(2cos^2 \theta -1)^2} = \frac{4 sin^2 \theta cos^2 \theta}{1+(4cos^4 \theta - 4 cos^2 \theta + 1)} = \frac{2sin^2 \theta cos^2 \theta}{2cos^2...
  41. D

    Creating 16-Bit Sine Table w/ 8-Bit Verilog & Sin Table

    How do I use two 8-bit sine table to make one 16-bit sine table? Here is my 8-bit sine table in verilog char sintable[256] for(int i=0;i<256;i++) sintable[i]=sin(2*pi*i/256)*128 I know I have to somehow use: sin(theta+ delta*theta) theta would be the first 8-bit and delta*theta...
  42. R

    Unravelling the History of Sin, Tan and Cos

    Can some one tell me how sin, tan and cos came about. I know the equations, but i want to know how it brought about.
  43. T

    How Do You Integrate 2x sin(x^2) dx?

    may i know how to integ [2x sin (x^2) dx]??the answer is -cos(x^2) thanx...
  44. T

    Is sin convergent or divergent

    I just have a quick question, is cos and sin divergent or convergent? I keep getting mixed results from different sources. I know that both functions oscillate so on the interval [0, infinity) they both diverge. But for some of my homework problems relating to improper integrals, the book...
  45. S

    Show that the functions sin x, sin 2x, sin 3x, are orthogonal

    Show that the functions sin x, sin 2x, sin 3x, ... are orthogonal on the interval (0,pi) with respect to p(x) = 1 (where p is supposed to be rho) i know i have to use this \int_{0}^{\pi} \phi (x) \ psi (x) \rho (x) dx = 0 and i have no trouble doing it for n = 1, and n=2 but how wouldi go...
  46. P

    Evaluating Limit: Sin(x + Sin x) at x=π

    Hello can someone help me with this question?? Use continuity to evaluate the limit: lim x->PI Sin(x + Sin x) Please! thanks
  47. N

    Inverse function of sin , cos and tan

    Solve the following question. Give your answer in cert form .Thank you . sin-1 x + sin-1 (2x) = pie/3
  48. R

    How do you get rid of the SIN() function to solve for x?

    i have x*sin(x/2) - 18/pi =0 and i need to solve for x.. how in the heck can i get rid of that sin() function? very confused.. any help will be appreicated..! btw.. i need the answer ASAP! thanks a lot guys
  49. M

    Proving Triangle Properties with Sin and Cos

    hey everyone, i have to show that in a triangle, there is : (A, B, C are the angles of that triangle) \sin \left( 1/2\,B \right) \cos \left( 1/2\,C \right) +\sin \left( 1/2 \,C \right) \cos \left( 1/2\,B \right) =\cos \left( 1/2\,A \right) for this one, here is what i got to...
  50. H

    Exploring Traveling Waves: Sin vs. Cos

    For the traveling wave described by the formula y(x,t) = Asin(kx-wt) Then the wave is traveling in the +x direction. True or false? In the physics textbook I have, it describes a traveling wave by y(x,t) = Acos(kx-wt), using COS instead of SIN. Is there a difference between these 2...
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