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. U

    Maximum value of F - SIN Waterloo Contest

    Homework Statement Superman is regaining his strength by pulling with a force F on a large block of mass M resting on a frictionless floor as shown. A small block of mass m rests on the upper surface of the large block, and there is friction at that surface, with static coefficient μ. Lois...
  2. D

    SIN Contest Water Tank in a Moving Vehicle Question

    Homework Statement Audrey McLaughlin has a vehicle with a built-in rectangular swimming pool. The pool is 2.4m long, 1.4m wide, and is partly filled with water to a constant depth of 1.2m as shown. Calculate the minimum additional height, h, to avoid water spillage when the vehicle maintains...
  3. F

    SIN contest: ballistic missile

    Homework Statement The problem and solution involving the ballistic missile question is in the attached picture. Homework Equations The Attempt at a Solution Why does the first expression have (24)(6) in the denominator, when the second expression has (24)(6)(2) ? My thought...
  4. E

    Integral sinc(a sin theta) knowing sinc, sinc^2 etc.

    Homework Statement Solve main lobe of radio telescope if the power diagram is given as: P_{n}(\vartheta, \varphi)=sinc^{2}(a*sin\vartheta) Homework Equations Ω_{m}=\int\intP_{n} sin\vartheta d\varthetad\varphi The Attempt at a Solution Purely math question - but I have problem...
  5. S

    Torque when to use cos and sin

    I have a issue with determining when to use cos and sin when calculating torque; For example. Referring to the attached picture. The SEESAW asks evaluate the torque of m2 (m2>>m1). For second part evaluate the torque... MY question: WHY in the first part (SEESAW) do they use cos...
  6. S

    Laplace's equation & Fourier series - I can use cos or sin?

    Homework Statement This is a question related to finding the velocity field of an incompressible fluid in a square pipe with sides at y = ±(a/2) and x = ± (a/2). It comes down to solving a homogenous equation which is also Laplace's equation \frac {δ^2 w(x,y)^H}{δ x^2} + \frac {δ^2...
  7. F

    Waterloo SIN contest question (springs and energy)

    Homework Statement Both the question and solution are on this link (Question 7): http://sin.uwaterloo.ca/solutions_2012.pdf I understand the solution they provided, but I think the question is misleading and should not have been worded that way. I just want to clarify if I'm right or not...
  8. E

    Use linear interpolation to estimate sin 36 using as your 'known' values 0 & 60?

    here is the answer: 36/60 = x/.8660 60x = .8660 x 36 60x = 31.176 x = .5196 however, where does the value: 0.8660 initially come from? any help would be appreciated
  9. H

    Why Does (sin(2x))/x Equal 2 as x Approaches 0?

    Homework Statement I have the equation (sin(2x))/x = ? The Attempt at a Solution I know that the answer to this is 2, but I am not sure why (sin(2x))/x = 2 Can somone explain? Thanks
  10. D

    Trig sin and cos graphs n00b help.

    Homework Statement Hi everyone. I understand the basics of trig graphing; but am having a hard time understanding f(x) first of all what to f and x stand for? Above and beyond that any help understanding f(x) or a link to a website that might help me would be great. Homework Equations...
  11. L

    Finding this limit involving sin and cos

    Homework Statement I have this function: f(x) = \frac{1}{x}-\frac{\cos{(x)}}{\sin{(x)}} For all x \in R where x \neq n \pi, n \in Z Ok I have to find the following limit: lim_{x\rightarrow0+}(f(x)) Homework Equations Limits in general and perhaps the always great...
  12. M

    What Values of x Solve the Equation sin(kx) = 0?

    Homework Statement sin(kx)=0 What describes the value of x. Homework Equations N/A The Attempt at a Solution I remember doing this last year but I forgot how to. kx=n(pi) x= n(pi)/k x=n(pi)/k + (pi)k/n where n is any integar Is this right?
  13. S

    Physical derivation of the Sin series

    I was reading feynman's lectures on physics and i came across the 23-2 in volume two where he is talking about a capacitor at high frequencies. He then uses the equations of E and M to come up with an approximation of the electric field between the two plates as the field oscillates at a high...
  14. N

    Minima of sin function with domain (a, b)

    Homework Statement Consider the function f(x) = sin (x) in the interval x ∈ (p/4, 7p/4). The number and location(s) of the local minima of this function are? Homework Equations The Attempt at a Solution I have managed to get one of the minimas (i.e. 3p/2), however i am unsure about...
  15. J

    Creating a square wave pulse at the peak of a sin wave

    Hi all, I am trying to create a square wave pulse that lasts for a relatively small amnount of time which corresponds (as close as possible) to the peak of a sin wave input of period about 1 second. The only way that I can think of doing this is via a programmable device such as an arduino...
  16. M

    Prove problem involving sec cos sin

    Hi guys been struggling to solve this If you know how to do it, please do solve and show work so that I can follow your steps Homework Statement prove (sec(x)-cos(x))/(sec(x)+cos(x))=(sin^2(x))/(1+cos^2(x))
  17. S

    Solving Sin (90+Theta) = Cos - Explanation

    i understand how sin90-theta is cos , but i am having trouble with sin 90+theta = cos ...please explain
  18. K

    Solve -sin 20° sin 40° sin 60° sin 80°sin 20° cos 30° sin 40°

    Solve - sin 20° sin 40° sin 60° sin 80° sin 20° cos 30° sin 40° cos 10° hmm...?
  19. J

    How Do You Find the Laurent Expansion of sin(z)/(z-1) at z=1?

    Homework Statement I'm supposed to find the Laurent expansion of sin z/(z-1) at z=1. The Attempt at a Solution I thought about expanding the sine as a power series of (z-1) but I'm not so sure if that would be correct since the sine is a function of z and not z-1.
  20. mesa

    Trying to figure out a single variable expression for Sin

    Well, I am now trying to figure out a single variable expression for Sin. I have a couple ideas using some pieces of geometric formulas I have played with recently but this is still new to me. I'm not talking about sin x, but an algebraic expression for the sin wave. Any thoughts?
  21. A

    MHB Proving/Disproving Equicontinuity of F_n(x) = sin nx

    Prove or disprove F_n(x) = sin nx is equicontinuous I know the definition of equicontinuous at x_0 it says for all \epsilon >0 there exist \delta>0 such that if d ( f(x_0),f(x) ) < \epsilon then d(x_0 , x) < \delta trying if it is equicontinuous at x_0 = 0 Given \epsilon > 0 | f(x)...
  22. X

    Vectors Using Cosine or Sin Law

    Homework Statement Need help with a question ... .__." q: if the magnitude of a=2 and the magnitude of 5a-2b= 7.7, and the angles between the vectors a and b is 50 degrees determine the magnitude of b. Homework Equations The Attempt at a Solution first I drew a diagram...
  23. B

    Sin and inverse sin multiplied

    Homework Statement Evaluate the following: Sin^-1(sin(19*pi/7) in terms of pi The Attempt at a Solution i can't see any other way apart from the functions cancel to give 19pi/7 but checking on wolfram gives 2*pi/7, can anybody explain or help? Thanks
  24. J

    MHB Sin Values of 87 and 89 Degrees

    The value of $\sin (1^0).\sin (3^0).\sin (5^0)...\sin (87^0).\sin (89^0)$ where all angles are in degree
  25. L

    Linear independence of sin (x), cos (x) and 1, proof

    What would be the best way to show that functions f(x)=1, g(x)=sin(x) and h(x)=cos(x) are linearly independent elements of the vector space \mathbb{R}^{\mathbb{R}}? I know that the linear independence means that an expression like \alpha \mathbb{x}_1 + \beta \mathbb{x}_2 + \gamma \mathbb{x}_3...
  26. C

    Use De Moivre's to express sin 4Theta

    Homework Statement Using De Moivre's formula to express sin 4θ in terms of sinθ and cosθ. Using this result, express sin4θcosθ in terms of sinθ only. Homework Equations The Attempt at a Solution So sin4θ = [cosθ+isinθ]^4 using Binomial ... cos4θ= cos^4(θ)...
  27. S

    Question about tan, cos, and sin

    So, I am trying to understand what tangent, cosine, and sine are in practical terms e.g. if something is tangent with something else we know it is touching that something. That seems like a practical definition of tangent to me. So, then what is a sine? what is cosine? I was thinking like...
  28. T

    How to graph a sin function with respect to it's limits and x intercepts

    I have been given a question to sketch the curve of y=sin(x). I have looked into finding the domain which I understand but I don't understand how I prove the x intercepts mathematically as when I make x=0 I obviously get a 0 value for y but a sin curve obviously intercepts and pi and 2pi etc...
  29. T

    Use the Sin Law to find angle C

    Homework Statement Use the Sin Law to find angle C sinC/45 = sin135/92.5 C = 20.1° How to get from equation to answer :confused:
  30. D

    Trigonometric equations with sin and cot

    Homework Statement find the value(s): cot(2sin^(-1) 2/7) The Attempt at a Solution I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came...
  31. P

    How can I find all possible angles for a given sine value?

    Homework Statement This is from a physics problem, but my question is more mathematically oriented. After working through the problem, I arrive at the last step. Sin(x)=.967 The question says that there are two possible angles for x. The Attempt at a Solution arcsin(.967)...
  32. U

    Identities sin, cos, tan etc. stuff

    Homework Statement ((cos x)/(1+sin x))+((1+sin x)/(cos x)) Homework EquationsThe Attempt at a Solution multiplied the left equation by (cos x)/(cos x) and the right fraction by (1+sin x)/(1+sin x) get ((cosx)^2 +(1+sinx)^2) / (1+sinx) (cos x) and I have no idea where to go from here
  33. M

    Limit involving sin at x=pi/6: Solving with Substitution Method

    Homework Statement find the limit: \lim_{x\rightarrow\frac{\pi}{6}}\frac{2sin(x)-1}{6x-\pi} The Attempt at a Solution Any starters please, I've tried the substitution method but went nowhere.I did x=(pi+h)/6. I still get 0 over something which is zero and i know that is not correct.
  34. R

    Help with 1 step in proof of d/dx sin x = cos x

    I understand everything in the proof except the last step I have written here. What comes after, I understand. How is it that the cosine and sine are able to be factored out of the fraction? That one step gets me. I was never too good with my trig, and have finally gotten a decent grasp of...
  35. P

    Cos & Sin: Learn How to Work With Them

    Yes, I have searched on google/youtube but I want to know how to work with them in tasks for example ramp friction ##f=mgcos0##
  36. L

    Reduction formulas for integral of sin and cos

    Integrate sin2(x)cos4(x)dx using reduction formulas? My book says integral sin2(x)cos4(x)dx= integral cos4(x)-integral cos6x dx Now the reduction formula for n=6 for integral cos6(x)dx= (1/6)cos5(x)sinx+(5/6) integral cos4(x)dx Here is the part I don't get: It then says ...
  37. D

    MHB Solving $\sin(z) = 2 + 3i$ using complex numbers

    What is the best way to handle $\sin(z) = 2 + 3i$? Option (1) $\sin(z) = \sin(x + yi) = \sin(x)\cos(yi) + \sin(yi)\cos(x) = \sin(x)\cosh(y) + i\sinh(y)\cos(x)$ $\sin(x)\cosh(y) = 2$ $\sinh(y)\cos(x) = 3$ Option (2) $\displaystyle\sin(z) = \frac{e^{zi}-e^{-zi}}{2i} = 2 + 3i$ Which option is...
  38. A

    Solving SIN, COS, TAN with a TI-30XA Calculator

    Hello, I'm having some problems. So for geometry class today, the teacher taught us this COS, SIN, TAN stuff. I got the concept how to get the fractions from the triangle and everything. Problem is how to plug it in the calculator. I have a basic TI-30XA, and I'm trying to plug in fractions...
  39. B

    What is the correct derivative of sin 5x?

    Homework Statement what is the derivative of sin 5x The Attempt at a Solution using the product rule, i think the answer would be cos 5x + sin 5 but the book says the answer is 5 cos 5x
  40. R

    Solving 10.0km + 5.0km [E15S] with Cos and Sin Laws

    Homework Statement 10.0km [N] + 5.0km [E15S] Homework Equations Cosine Law The Attempt at a Solution If you draw it out you see that 10km is 90 degrees north. From the 10km end, you do E15S for 5km. Therefore, a = 10km, b = 5km, c = ?, C = 90 - 15 = 75. Therefore: c^2...
  41. B

    Derivative of x sin x: Why Isn't the Answer x cos x?

    Homework Statement differentiate f(x)= x sin x Homework Equations The Attempt at a Solution The answer is x cos x + (sin x) * 1 I thought the derivative of sine was cosine. So why isn't the answer x cos x?
  42. A

    Mathematica Mathematica: Fourier Transform by hand of sin

    Hi, i do not understand why i can find the FT of sin in mathematica using the built in function but not by integrating, even thoiugh they should be the same: Integrate[Exp[i(ω-ω0) t,{t, -∞, ∞}, Assumptions ->ω0 el Reals && ω el Reals] but the statement FourierTransform[Sin[ω0 x]...
  43. S

    Physics kinematics SIN question

    Homework Statement A car, traveling at a constant speed of 30m/s along a straight road, passes a police car parked at the side of the road. At the instant the speeding car passes the police car, the police car starts to accelerate in the same direction as the speeding car. What is the speed...
  44. T

    Position in Motion: When to Use Cos & Sin in x=A*sin(wt+phi) or x=A*cos(wt+phi)?

    In what kind of cases do u we formulate the equation type x=Asin(wt+phi) or x=Acos(wt+phi)...and if for example we use it to define the position of some thing in motion when do we know when to use cos and when to use sin...?
  45. Z

    Eqn for SHM, sin function, so why cos?

    I had thought the eqn of simple harmonic motion is a sinusoidal function of time, with the eqn being: x(t) = A sin(wt + ∅0) Halfway down this page: http://electron9.phys.utk.edu/phys135d/modules/m9/oscillations.htm in Problems: in solution (a) it gives; The displacement as a...
  46. B

    Complex Analysis Integration with Sin and Cos

    Homework Statement Compute the integral from 0 to 2∏ of: sin(i*ln(2e^(iθ)))*ie^(iθ)/(8e^(3iθ)-1) dθ (Sorry for the mess, I don't know how to use latex) Homework Equations dθ=dz/iz sinθ = (z - z^(-1))/2i The Attempt at a Solution So I tried to change it into a contour integral of a...
  47. T

    Graphing Sin Functions: Calculator Tips and Tricks for y=sin(c(x-d))

    Homework Statement This may seem like a stupid question so i apologize. This is the general form for the said equation: y=sin c (x-d) c= 28 d=3 How would i enter this into my calculator (ti 84) to graph it?? Homework Equations The Attempt at a Solution y=sin...
  48. V

    How can I integrate 1/(sin x + sec x)?

    Homework Statement ∫ 1 /( sin x + sec x) dx Homework Equations The Attempt at a Solution ∫ cos x / ( sin x + cos x ) style question Tried ∫ cos x / (sin x . cos x + 1) dx and uses sin 2x tried substitutions nothing seem to work
  49. K

    Solving "sin 2x = sin 2y" with Double Angle Identity

    Homework Statement I'm stuck on a question that results in this equality sin 2x = sin 2y how do I solve that for x or y? the only identity is the double angle one I can use I think but I don't know how that would help. Homework Equations The Attempt at a Solution
  50. D

    Solving an Equation with Sin -1 and Sin: Confusion and Help Needed

    this example was in a book I bought ( maths methods for physics, Mathews and Walker) dy/dx + sqrt( (1-y^2) / (1-x^2) ) = 0 dy/(1-y^2) + dx/(1-x^2) = 0 sin -1 y + sin -1 x = c [1] or, taking the sine of both sides x (1-y^2)^1/2 + y...
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