Sin Definition and 452 Threads

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. 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...
  2. O

    How to get θ sin and cos are together in 1 equation

    b2cos2θ+2cosθ(-mb+bc2-bz-bcsinθ)+2sinθ(cm-cz)-c2sin2θ=p How to get θ in terms of b,c,m,z,p The equation i formed to calculate the dynamic PLs, anyone can help to solve this, i would much appreciate! I am doing my FYP!
  3. J

    Approaching the Limit of a Sin Function Using Calculus Techniques

    Homework Statement [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP120619i0ea2h15bci31300005d9a3422292h43h4?MSPStoreType=image/gif&s=43&w=174&h=39 Homework Equations The Attempt at a Solution So Wolfram says to use L'Hopital as the first step, we haven't learned anything about this...
  4. W

    Exponential function integral with Sin as its index

    Integral descriptive: \int _{0}^{\pi }\! \left( a+{\it k1}\,\sin \left( \theta+{\it beta1} \right) \right) {e}^{{\it k2}\,\sin \left( \theta+{\it beta2} \right) }{d\theta} I think if beta1 and beta2 come to zero,i may be a typical integral.However,in this integral,beta1 and beta2 are...
  5. J

    Schools Do grad schools consider varied research interests a sin?

    I'll be applying to grad schools in the coming months, and I'm mostly interested in programs that involve nonlinear dynamics, synchrony, and chaos. But, my undergraduate research is in two other areas, different from each other and not involving nonlinear dynamics at all. I've worked on...
  6. J

    How to prove that sin square x cos square x is identical

    Homework Statement 1) how to prove that sin square x cos square x is identical to 1/8 (1- cos 4x)? 2) f(x) = x square +7x -6 ----------------, show that when x is sufficiently small for (x-1)(x-2)(x+1) x^4 and higher powers to be neglected. Homework Equations 1) cos (s +...
  7. D

    What is the correct way to solve the integral of cos^5 x sin x?

    When I did this problem I overlooked the fact that a u-sub of u=cos x would work fine. I ended up using the more complicated trig integrals rules and did this: ∫cos5 x sin x dx ∫(cos2 x)2 cos x sin x dx ∫(1 - sin2 x)2 cos x sin x dx ∫(sin5 x - 2 sin3 + sin x) cos x dx with u = sin x, du =...
  8. A

    Understanding the Sin of an Angle: θ and 90°

    sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?
  9. nukeman

    Tangential and Radial acceleration - Sin and Cos simple question

    Homework Statement Im confused about something. Ill post the answer sheet to a question. It has all the data you need. BELOW: NOW... for Tangential component of the acceleration, WHY did they pick cos? and for Radial, WHY did they pick sin? I am starting to do a lot of FBD to equations...
  10. L

    Trouble plotting a simple sin function

    So all I'm trying to do is plot y = (2sin(3w))/w, w is the angular frequency. I basically want this graph in radians. So this is what I did at first: >> x = [0:.01:20] ; //want bounds from 0 to 20 y = 2.*((sin(3.*x))/x); plot(y) But when I do this I get a graph of nothing, I assumed...
  11. S

    Use the cross product to find the sin of an angle then prove it

    Homework Statement Leta theta be the angle between the vectors u=2i +3j -6k and v=2i + 3j+6k A) use the dot product to find cos theta b) use the cross product to find sin theta c) confirm that sin^2(theta) + cos^2(theta)=1The Attempt at a Solution I got a to be 117 degrees, but however b and c...
  12. M

    Inverse hyperbolic sin derivation

    Homework Statement derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x Homework Equations sinhx=(e^x-e^-x)/2 ? The Attempt at a Solution i have been staring at this for awhile and i don't know how to start what should be the first step towards deriving that...
  13. M

    Fortran Truncated Sin Series in FORTRAN

    I am very much confused and frustrated at this point and would just like to understand what I'm doing wrong... This program is supposed to calculate a truncated value of sine using it's series expansion beginning at i = 1. At values under 20 degrees it compares almost exactly with the intrinsic...
  14. A

    Two integral problems including e and sin

    1. ∫ 6e^(-y/4) dy 2. ∫ [ sin(pi x) - (3/x) ] dx Any help with either of these would be great. I'm teaching myself integrals for Physics C and i have absolutely no clue what to do with these. Thanks in advance
  15. L

    Proving Sin and Cos Values of pi/6: Analytical Solutions

    I'm currently reading Apostol's Calculus. I'm now on the part where I need to prove sin and cos values for specific values. Right now I'm working on sin and cos of pi/6. However, I always get at 1/2 and √3/2 for the final value. Here's my solution so far: Homework Statement Use the properties...
  16. D

    How can we find the true solution for cosh x = tanh x?

    According to Wolfram Alpha, if sin x =cosh x then x=-(\frac{3\pi}{4}+\frac{3i\pi}{4}) But how do you derive this? Also, what is the solution to cos x = sinh x in exact form? Thanks.
  17. Saitama

    Solving a Sin Equation: Find Value of cos6x-4cos4x+8cos2x

    Homework Statement If sin x + sin2x + sin3x= 1, then find out the value of cos6x-4cos4x+8cos2x. Homework Equations The Attempt at a Solution How should i start? :confused: I don't find any way to convert them to cos 6x or cos 4x.
  18. L

    Limits of log sin equal to 0/1/infinity?

    Homework Statement limx->\pi/2(ln sin x)/((\pi-2x)2)Homework Equations The Attempt at a Solution Putting \pi/2 into this equation gives 0/0, however, the limit of this could be 1,0 or infinity, so how would you distinguish between the three?
  19. J

    Line integral of sin cos function

    Homework Statement integral (sin^4(x) + cos^4(x))^.5 dx Homework Equations sin^2(x) = (1 - cos^2(x)) The Attempt at a Solution cos^4(x) + {1 - cos^2(x)}^2 = 2cos^4(x) -2cos^2(x) + 1 subst u = cos^2(x) integral (2u^2 - 2u +1)^.5
  20. nukeman

    Pythagorean Identities - finding sin and cos ?

    Homework Statement For tan(theta) = /2/3 (theta in quadrant 2) find sin(pheta) and cos(pheta) using the pythagorean identities. Homework Equations The Attempt at a Solution Which 2 pythagorean identities would I use? My trouble is with finding sin and cos from tan.
  21. nukeman

    Im stuck Question a bout graphing sin and plotting points

    Homework Statement Im doing a question where I have to graphc y = -4 sin x Ok well I got the period and amplitude, so I have the interval of [0, 2pi] Now, in order to plot points, I have to divide the interval into 4 sub intervals. I don't understand how I do that! This is where I...
  22. N

    Need help with determing domains of sin, cos, and tan

    Homework Statement Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses. i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)...
  23. I

    Graphing Sin Functions with Phase Shift and Vertical Shift | Period of 6π

    Homework Statement y=-2+sin((\frac{\Theta}{3})-(\frac{\pi}{12})) Homework Equations The Attempt at a Solution [PLAIN]http://img715.imageshack.us/img715/7707/trigg.png Phase shift: \frac{\pi}{4} Vertical shift: -2 Period: 6\pi
  24. A

    What is the solution to finding the sum of square sin() functions?

    Hi all, I work as monitor for a pre-university course and one student showed me this problem: Homework Statement To find how much is y: y=sin2(10)+sin2(20)+sin2(30)+...+sin2(80)+sin2(90) Homework Equations I don't know. I thought about sen2x+cos2x=1 The Attempt at a Solution To...
  25. R

    2nd order ODE with Sin function.

    Hey guys! I'm trying to solve a 2nd order differential equation. I am quite familiar with the method of solving these equations like treat them like characteristic equation ODE. but there's a question which I really want to solve. question is d^2 X/dt^2 +dX/dt +sinX=0. How should I solve this??
  26. G

    Proving a^2+b^2=1 has Only One sin* & cos*

    Doing a past paper where long story short I have a set of equations and I have to prove the variables are equal to some trig function. Namely: a^2 + c^2 = b^2 + d^2 = 1 ad - bc = ab + cd = 0 Now I know that sin^2 + cos^2 = 1 and that sin(A+B)=sinAcosB + cosAsinB, etc and the...
  27. S

    Limit of a product of sin and a polynomial

    Homework Statement Given a n-sided polygon. Divide it into multiple small triangles that have same radius r. Compute the following limits: Homework Equations The Attempt at a Solution When I plug in a random number to guess the answer, somehow it is always near 0 (very small) so...
  28. N

    Solve for Theta: How to Divide Sin?

    Homework Statement Its a word problem but I will just state everything here in simple form. Given ------------ V initial = 100ft/s r=300ft r= 1/32 V^2 Sin 2theta Unknown --------- Solve for theta The Attempt at a Solution 300=1/32 (100)^2 sin 2theta 300= 1/32 (10000) sin 2theta 300= 312.5...
  29. N

    Solving sin z=2: Equating Real and Imaginary Parts

    Homework Statement Solve sin z=2 by (a) equating the real and imaginary parts (b) using the formula for arcsin z. Homework Equations (a) sin z = sin x * cosh y + i * cos x * sinh y arccosh z = log[z + sqrt(z^2 - 1)] (b) arcsin z = -i * log [i * z + sqrt(1 - z^2)] The...
  30. L

    Cosine, Sin, Tangent when find force/tension

    Ok... so I had this down and now I am all confused ;/ I am not posting in the homework sections because its not for homework although I will gie an example of a problem... I just want to understand why/how they use these to find the force/tension... Example: A 20 kg loudspeaker is...
  31. J

    Orthogonality of Cosine and Sine Functions: A Proof by Explicit Integration

    Homework Statement This would be easier if I knew how to use LaTeX, but I'll give it a shot. Show by explicit integration that the following is true: Integral from 0 to a of sin(m*pi*x/a)*cos(n*pi*x/a)=0Homework Equations The Attempt at a Solution I've used an identity to change...
  32. C

    Exploring Sin & Cos: Is 1/sec equal to cosin?

    Homework Statement Sin^{2} 20\circ + 1/sec^{2} 20\circ = 1 ? Because isn't 1/sec the same as cosin? Homework Equations The Attempt at a Solution
  33. C

    Solve Sin pi/12= 1/4 (√6 - √2)

    Sin pi/12= 1/4 (√6 - √2) ? I took sin pi/12 = sin (4pi / 12 - 3pi/12) = sin (pi/3 - pi/4) Did I do this right?
  34. T

    Deriving equations involving sin and cos

    Homework Statement I'm asked to derive equation(2) from equation(1). equation(1): d=(tsin(2i))/((n^2-sin(i)^2)^1/2) equation(2): n=sin(i)(((2tcos(i/d))^2+1)^1/2) Homework Equations The Attempt at a Solution My attempts have got me nowhere, and I don't know how to even...
  35. T

    Deriving equations involving sin and cos

    Homework Statement This problem deals with the displacement of a light ray as it travels through a glass medium. Starting with the equation #1: d=S[sin(i)cos(r)-cos(i)sin(r)] (where d=the length of displacement of the light ray in the glass medium, i=angle of incidence...
  36. H

    Integrating functions of sin to a power

    Homework Statement Integrate sin5(x/3)dx on the interval [0,pi] Homework Equations sin2(x)=1-cos2(x) dcos(x)dx=-sin(x) The Attempt at a Solution I split off one of the sins and then set my integral equal to (sin2(x/3))2*sin(x/3) switching in 1-cos2(x/3) afterward. Then I set u =...
  37. N

    Why does tanθ = 1/2 > 0 and sin θ mean that it lies in quadrant 3

    why does tanθ = 1/2 > 0 and sin θ" mean that it lies in quadrant 3 Homework Statement Given one value of a trigonometric function, and the sign of another, find the remaining ones Given that tanθ = 1/2 > 0 and sin θ < 0 , the point P = (x,y) that corresponds to θ , lies in quadrant 3 Homework...
  38. S

    Determining Theta in Sin Ratio: Why the Difference?

    Homework Statement The ratio sin theta =-12/13 Homework Equations The Attempt at a Solution which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees this answer is legitimate but another way of writing...
  39. N

    Percent Difference Between Theta and Sin (Theta) help

    Homework Statement This is what my professor is asking me to do: Show a table for when sin(theta) and theta have a percent difference of 1%, 5%, and 10%. (i.e. this table will have three columns)" You are to show this table (for all three quantities) such that the behavior leading slightly...
  40. J

    When to Use Sin and Cos in Projectile Motion Calculations?

    Homework Statement This is a more general question... but here is a specific example in which I don't know why sin is used where it is and why cos is used where it is. I don't need the problem worked out or anything (I have it worked out by my professor), I just need to understand why sin and...
  41. V

    Why is the derivative of sin x / x at x=0 1?

    Homework Statement Why is sin x / x at x = 0 equal to 1? Homework Equations d/dx (sinc(x)) evaluated at x = 0. The Attempt at a Solution El hopital's rule Cos(x)/1, cos(0) = 1 However when looking at the picture of Sinc, http://www.wolframalpha.com/input/?i=sin(x)/x, it...
  42. C

    Why Does the Solution Include √13 in the Numerator for Trigonometric Ratios?

    Ok... (2, -3) R = (Sqrt x^2 + y^2) R = (sqrt (2)^2 + (-3)^2) R= (sqrt 13)^2 R=13 Sin = y/r Sin -3 / 13 ? Cosin 2 / 13 ? But then.. how come the answer gives me sin -3 (sqrt13) / 13 and for cosin 2(sqrt13) / 13 My question is how come there's a (sqrt13) included for the...
  43. S

    Euler's formula & expressing combinations of sin and cos as cos

    I have a rather difficult math problem. In my circuits class the professor prefers to express the cosine function using Euler's formula as (ejwt+ejwt)/2. Last semester for the final, one of the problem's solutions (that he gave us) used partial fraction decomposition to solve the Laplace...
  44. M

    Writing Sin Equation Homework: Finding Amplitude, Upward Shift & Phase Shift

    Homework Statement I have to fill in the missing info... Y=A*Sin[B(x-c)] +D A = 3. For finding the amplitude all I have to do it multiply 1/2 by the range? D = 3. For finding upward shift all I have to do is see if the center has moved up? period = 4pi/3 so B = 3/2 I am confused on...
  45. B

    Finding the First Three Terms of exp(z sin z) Taylor Series

    find the first three non zero terms in the Taylor Series about z=0 of exp(z sin z) i have little idea how to even start on the question because it is exp to the power of z sin z and it just looks too complicated. i hav tried looking thru txtbooks for something similar but no similar question...
  46. C

    What is the Derivative of sin x^5?

    Find the derivative. d/dx \int\stackrel{x^5}{o} sint dt I came up with sin x^5. The answer is 5x^4 sin (x^5). Not sure what I'm missing here.
  47. A

    What is causing the discrepancy between the Hermite curve and the sine function?

    So I have a Hermite curve with the control points: //point# (x,y): p0 (1,0) p1 (1,(Math.sqrt(2)-1)) p2 (Math.sqrt(0.5), Math.sqrt(0.5)) I also have a very basic algorithm to find the point on the locus at a given degree between 0 and 45 degrees using the control points. I could...
  48. R

    Is the Inverse Function Theorem Applicable to Complex Arcsin on C-{Pi/2+k*Pi}?

    It seems to me that the standard definition of the complex Arcsin (the principal branch) is something like this: [PLAIN]http://math.fullerton.edu/mathews/c2003/maptrigonometricfun/MapTrigonometricFunMod/Images/mat1017.gif Anyways, it's defined as a map from C-{z in R : |z|>=1} to the strip...
  49. P

    Integral inequality with sin proof

    Homework Statement prove that for all x>0 Homework Equations -1 \leq sin t \leq 1 The Attempt at a Solution the area under the graph is increasing as x increases also, i tried to write it the sigma way: then take the limit as n-->infinity i got stuck trying to figure out how to...
  50. J

    Derivatives, Sin and Cos, Rate of Change, Tangent Lines

    Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers! Let f(x)=−3x+6 if x<-3 = 15 if x > -3 Find the average rate of change of f(x) on the interval −5<x<5 . The average rate of...
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