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. K

    [Fourier transform] Convolution product with sin and cos

    I'm asked to transform y(t) = x(t)*x(t) (where * is the convolution product) and x(t)= sinc(t)cos(2π10t) ( sinc(t)= sin(πt)/(πt) ).The attempt at a solution Clearly everything is simple if you know X(f), because y(t)=InverseFourier{ X(f)2 }. The problem is that I can't find X(f). By the way...
  2. M

    Snell's Law: From n sin theta to n1sintheta1 = n2sintheta2

    Hi, I'm new to the forum as I'm struggling to find answers with an internet search. I've seen Snell's Law stated as n sin theta = constant. How does this arise from its more familiar form of n1sintheta1 = n2sintheta2? I can't work it out. Thanks for reading!
  3. S

    Proving Sin x + Sin 2x + Cos x + Cos 2x = 2√2cos(x/2)sin(3x/2+π/4)

    Homework Statement Prove that: ##sin x + sin 2x + cos x + cos 2x = 2\sqrt{2} cos (\frac{x}{2}) sin(\frac{3x}{2}+\frac{\pi}{4})## Homework Equations We know all the double, compound, and half angle formulas. The Attempt at a Solution Taking on the RHS, we have Expanding with half angle...
  4. M

    Why use cos for dot product and sin for cross product?

    Dose anybody knw that why we take cos with dot product and Sin with cross product?
  5. P

    Is there an equivalent of cosx=1-(x^2/2) for the sin function

    Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)
  6. T

    MHB Determining the sin theta, tan theta and cos theta at P (x,y)

    Determine the values of sin v, cos v, and tan v at each point P(x, y) on the terminal arm of an angle v in standard position. (b) (3, 4) ( (d) (12, 5) (f) (7, 24) for b I was able to do tan \theta= y/x tan \theta= 4/3 \theta = 53.13 My textbook says I am wrong... doing an online...
  7. Sneakatone

    Can Differential Equations with Boundary Conditions Have Non-Unique Solutions?

    Homework Statement The given two-parameter family is a solution of the indicated differential equation on the interval (−infinity, infinity). Determine whether a member of the family can be found that satisfies the boundary conditions. (If yes, enter the solution. If an answer does not exist...
  8. T

    How can a horizontal component be of sin? Error in book or my brain?

    I've learned that the horizontal component is F cos angle not F sin angle, but I'm looking right now into the aqa physics a student book from nelson thrones, chapter 2.3 page 27, and it says that the horizontal components going to be made up of sin and the vertical out of cos... This is about...
  9. M

    Understanding Physics Symbols: Cos∠ and Sin∠

    Hi, I just started the chapter work and kinetic energy in my physics book, and I'm uncertain about the meaning of two symbols. They are 'F sub "two vertical lines"' and 'F sub "an upside down T/perpendicular symbol"'? Does it mean cos∠ and sin∠, respectively? Nevermind, I figured it out...
  10. vjacheslav

    Exact Sin Calculus: Solving for Trigon Funcs Without Triangles

    Hi! While computer programming Us encountered problem of exact calculus of trigonometry funcs. As is well known, all calculators and comp progs do x for Sin and x^2/2 for Cos on 0..Pi/2 and so on. It seems insufficient. While solving - next problem: trigon func definition without triangle.
  11. BeautifulLight

    Solving for Sin with no calculator

    Solving for Sin with no calculator + additional questions Sinθ=opp/hyp Sinθ=5/3 Sinθ=1.6 I know the answer is 35.87°. I would like to convert 1.6 to 35.87° but am unsure how.
  12. M

    Relating integral of powers of Sin b/w 0 and pi/2 to factorial form

    Our integral \int\limits_0^{\pi/2} \sin^{2a+1}(x)\,dx Has a Factorial Form: {(2^a a!)}^2 \over (2a+1)! What is the process behind going from that integral to that factorial form? My approach which is not very insightful: I used mathematica to calculate the integral to return...
  13. N

    What is the solution for Ry in Sin 0=Ry/Rx when given values for Rx and theta?

    Teacher assigned this on first day due tomorrow and i have no clue on some like this one: Sin 0=Ry/Rx a.) solve for Ry b.) solve for Rx c.) solve for 0 ?
  14. johann1301

    How do you solve sin x - 2x = 0 ?

    Homework Statement solve sin x - 2x = 0 The Attempt at a Solution I can see that zero is a solution, but i don't know how to actually solve it in a general way. Can somebody give me a hint?
  15. Dethrone

    MHB Calculating sin ( 0.5 arcsinx)

    I did this question using two different trig identities, each of which gave me a different answer when I graphed them on Wolfram Alpha. 1. First identity: sinx = 2sin(0.5x)cos(0.5x) isolating for sin(0.5x): sin(0.5x) = (sinx) / (2cos(0.5x)) The question wants sin (0.5 arcsinx): Applying...
  16. T

    Determining Sin wave horizontal shift 'C' value

    Find the equation of a sine function with its first positive maximum point at (pi/5,8) and its next minimum point at (7pi/10,-2). With the sin form as y=a*sin[b*(x-c)] + d I found: a=[max-min]/2 = 5 b= 2pi/period= 2pi/(2*[max-min])=2 d=max+min/2=3 I am having troubles determining...
  17. S

    Write sin in terms of Hermite polynomials

    Homework Statement Write ##sin(ax)## for ##a \in \mathbb{R}##. (Use generating function for appropriate ##z##) Homework Equations ##e^{2xz-z^2}=\sum _{n=0}^{\infty }\frac{H_n(x)}{n!}z^n## The Attempt at a Solution No idea what to do. My idea was that since...
  18. C

    Which angle is theta and when do I use sin or cos?

    Not a direct problem but this is a homework related question so I'm posting it here. When getting components with respect to gravity it is often intuitive, this isn't always the case. None of my classes thus far have talked about why when to use sin or cos, they just do. I'm wondering how I can...
  19. bsmithysmith

    MHB How to find the Double Angle formula for Sin given only a triangle

    I know the Double Angle for Sine is: \sin(2x) = 2\sin(x) \cos(x) but from the triangle given, how do I figure it out? We did this in class, but the teacher just told a small amount of things, and then let us talk amongst each other to solve it. Nearly all the students were glossy eyed and did...
  20. J

    Find the value of a complex number of sin and cos?

    Homework Statement fnd 1+i\sqrt{3}/1+i knowing sin ∏/12 cos ∏/12 Homework Equations The Attempt at a Solution Our teacher did not really teached me how to do it...
  21. M

    Proving the Validity of Sin, Cos, and Tan Equations in Right Triangles

    hello! we know that in every right triangle there are the sin, cos, tan etc equations how do we prove that these equations are valid? eg. how do we prove that the adjacent of an angle divided by the hypotenuse of the triangle is always the same for that given angle? thanks
  22. F

    Why is Sin the convention for the harmonic oscillator?

    In the course of solving the simple harmonic oscillator, one reaches a fork in the road. x(t) = A1Sin(wt) + A2Cos(wt) At this point, you exploit a trig identity and arrive at one of two solutions x(t) = B1Sin(wt+phi1) or x(t) = B2Cos(wt+phi2) Both of these are correct solutions...
  23. T

    Complex Sin value greater than 1

    Hi, My Complex Euler stuff is a bit rusty but I'm working on a problem (that I won't mention here) but I'm after an explanation as to how: Sin (theta) = 3.08 and so Cos (theta) = -i*2.91 What's throwing me is that I know Sin can only have a max at 1 trigonometrically (obviously) so I'm...
  24. S

    Finding second derivative of sin y+cos y=x in terms of x

    Homework Statement Find the second derivative of sin y+cos y=x, giving your answer in terms of x. Homework Equations Implicit derivatives The Attempt at a Solution ##\sin y+\cos y=x## ##\cos y \frac{dy}{dx} -\sin y \frac{dy}{dx}=1## ##\frac{dy}{dx}=\frac{1}{\cos y-\sin y}##...
  25. datafiend

    Solve the Sin Equation: Amp, Period, Phase Shift, Vert Shift

    Homework Statement Find the amplitude, period, phase shift, and vertical shift Homework Equations y=- 1/2sin [3 (x-∏/2)] -2 The Attempt at a Solution amp = -1/2, vertical shift is 2 down y-axis. I can't get the period and ph. shift.
  26. R

    Find arcsine(-2) using the rectangular representation of sin w

    Homework Statement Find \sin^{-1}(-2) by writing [tex]sin w = -2[/itex] and using the rectangular representation of \sin w Homework Equations Rectangular representation of \sin w The Attempt at a Solution I think my biggest problem here is I have literally no idea what the...
  27. B

    Finding Limit as x-> 0 of sin and cos equation

    Homework Statement lim (-x + sin(sinx))/(x(-1 + cos(sinx))) x-> 0 Homework Equations sinθ/θ=1 as θ-> 0 Squeeze Theorem? The Attempt at a Solution Well I've tried doing L'Hopital's rule, but to no avail. Each subsequent derivative just makes the equation nastier and more convoluted...
  28. B

    Why does Sin represent Y on unit circle

    As the title inquires, I am curious as to how or why the Sin function represents y coordinate on the unit circle.
  29. B

    Electric Field Problem (why don't I multiply by sin and cos?)

    Homework Statement In the figure the three particles are fixed in place and have charges q1 = q2 = +e and q3 = 2e. Distance a = 6.00 µm. What is the magnitude of the net electric field at point P due to the particles? Homework Equations E = k*q/r^2 The Attempt at a Solution I...
  30. M

    Need explanation about sin rule

    Hello. This is part of a solution but I don't understand the underlined part. Why is it equals to 0?
  31. C

    Sin theta= sin theta tan theta

    Problem statement Solve each equation over the domain theta greater than or equal to 0, less than or equal to 2 pi: Sin theta= sin theta tan theta Revelant equations Problem statement I divided it by sin theta to get tan theta equal to 1. Tan theta=1 can occur in the first and third...
  32. alyafey22

    MHB What is the relationship between the Mellin transform and the sine function?

    Mellin transform of sine Define the Mellin transform as \mathcal{MT}\{f(t)\}=\int^\infty_0 t^{z-1} f(t) dt where z\in \mathbb{C}If the transform exists , it is analytic in some vertical strip a<\mathrm{Re}(z)<b in the complex plane Find the vertical strip of \mathcal{MT}\{ \sin(t)\}...
  33. srfriggen

    Solving arcsin(√2) with Hyperbolic Sin Function

    Homework Statement What is arcsin(√2)? The Attempt at a Solution sin-1(√2)=a+bi sin(a+bi)=√2 ...expressing as hyperbolic sin function: -i*sinh(-b+ai)=√2 sinh(-b+ai)=-(√2)/i ...using the definition of the sin hyperbolic function: (e-b+ai-eb-ai)/2 = -(√2)/i...
  34. Omega0

    Simple Integration Orthogonal Sin

    Hi, take the function I(m,n) = Integral from 0 to 1 of sin(m*pi*x)*sin(n*pi*x) over dx depending from n and m, being +-1, +-2, and so on. If I use sin(x)sin(y)=1/2(cos(x-y)-cos(x+y)) I get sin^2(n*pi*x)=1/2-1/2cos(2n*pi*x) or I(n,n)=1/2 because the integral of cosine over full...
  35. N

    Find all solutions of sin on the interval

    Homework Statement i have solve 7sin(2x)-13sin(x)=0 for all solutions 0≤X<2p I used the double angle formula for sin(2x)=2sin(x)cos(x) The Attempt at a Solution I'm getting stuck near the end 7(2sin(x)cos(x)-13sin(x)) 14sin(x)cos(x)-13sin(x) now I am stuck
  36. U

    Complex Fourier series of sin (t)

    In finding Cn, I arrived at a different answer. I got an extra factor of (1/i) instead, which came when you do the integral of each exponential with respect to t; so you get a factor of 1/i(1-n) and 1/i(1+n) respectively.. Did they intentionally leave that out?
  37. N

    How Do You Solve the Equation 20sin(t)cos(t) = -4cos(t) for t?

    Homework Statement 20sin(t)cos(t)=-4cos(t) Homework Equations The Attempt at a Solution I added the cos to the other side but I am kind of stuck what to do. My instructor never really went over this well enough. Ugh..
  38. W

    Find sin, cos, and tan for a given quadrant angle

    Find (a) sin ∅, (b) cos ∅, and (c) tan ∅ for the given quadrantal angle. If the value is undefined, write “undefined.” My quadrantal angle is -450° Sin = opp/hyp Cos= adj/hyp Tan= opp/adj I drew a graph and put the angle -450° in the 3rd quadrant because both x and y are negative and I...
  39. J

    MHB Find Fourier Sin Series for f(x)=1, 0 < x < c

    3. Fourier sin series for f(x) = 1, 0 < x < pi is given by 1 = 4/n E 1/ (2n-1) times sin (2n-1) x, (0 < x < n). Using this, find the Fourier sinc series for f(x)= 1, on 0 < x < c where c > 0. Then find the Fourier series for g(x), x > 0 where g(x) = 1, 0 < x < c, -1, c < x < 2c, g (x + 2c)...
  40. K

    How to calculate Derivative of sin sq. root x by definition?

    Homework Statement Evaluate derivative of (sin sq. root x) w.r.t x? Homework Equations Limit Δx--> 0 (sin√(x+Δx) - sin(√x)) / Δx The Attempt at a Solution i couldn't operate it from here... Δy = (2cos((√x+Δx) + (√x)) . sin((√x+Δx) - (√x)) / Δx...?
  41. H

    Lowest value that can get the sin and the cos

    lowest value that can get the "sin" and the "cos" Sorry for my stupid question,but I forgot them. What is the biggest and the lowest value that can get the "sin" and the "cos" Thanks!
  42. dwn

    What is the velocity and direction of a transverse wave on a string?

    Homework Statement A transverse wave travels on a string whose mass density is    kg/m. The displacement (in meters) is given as a function of time and position as:     D(x,t) = 1.5sin(3x-24t+90°)  What is the velocity and direction of the wave? What is the speed of...
  43. S

    A particle is vibrating with f : Ut = 8 sin (1/2 pi t/T)

    from this equation i get the amplitude is 8 cm, it's a sine function so i guess it has to be a harmonic oscillation i haven't had physics in a while so not really getting anywhere -i need to know T (time for one oscillation) -the frequency f which is 1/T -Vt and At equations, i know i...
  44. V

    How To Find The Integral of Sin x dx?

    How to find the integral of sin x dx? $$\int sin x dx=?$$
  45. E

    Questions on Values of Exp, Ln, Sin & Cos

    hi every one .. i have some question 1 - why the value of exp = 2.71 ?? were from they get this value ? any derive or rule ? 2 - who i can fiend the value of ln and exp and sin or cos without using calculator ? like cos 56 sin 28 ?? or ln 24 ? exp 33 ? without using...
  46. D

    Describing electromagnetic radiation, why is there a second sin term?

    Homework Statement Hey all, I am working through a derivation that my professor gave me to do and I am having trouble understanding one of the formulas that he gave me, namely: "EM waves can be described as: E(x, t) = Eosin(2πx/λ)*sin(2πc/λ)" The the Eo*sin(2πx/λ) term makes sense to...
  47. S

    Why derivative of sin x is cos x, only if x is in radians?

    What differente does it make? As far as I can see it, the limit definition of a derivative shouldn't be affected by the fact that x is expressed in radians or degrees...
  48. A

    MHB How can the second term be mathematically turned into -j or 1/j?

    Hi all I am trying to go through and understand the derivation of \[X_{c} = \frac{1}{j\omega C}\] Where $X_{c}$ is capacitive reactance in ohms, $\omega$ is the angular velocity or $2\pi frequency$ and $C$ is capacitance in FaradsTo start with we already have $I=C\frac{dv}{dt}$...
  49. Saxby

    Why Do Wave Equations Use Sinθ and Cosθ Interchangeably?

    Why do some wave equations use sinθ and others cosθ? Does it make a difference when calculating properties such as wavelength and wave number? For example: y(x,t) = Asin(ωt+kx) y(x,t) = Acos(ωt+kx)
  50. F

    SIN contest Tension and Acceleration question

    Homework Statement The problem and solution are attached, but I don't think the solution is correct. Homework Equations The Attempt at a Solution The only thing I don't understand is why Joe needs to supply the force to move both people. It seems to me that gravity is providing...
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