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. T

    How do I solve the Sin 3x equation?

    no clue how to start this: show sin 3x = 3 sin x - 4 sin^3 x
  2. J

    Prove: (tan y + Cot y) sin y cos y = 1

    Hi, I need to prove: (tan y + Cot y) sin y cos y = 1 I've gotten this far and got stuck: (tany + cos y) sin y cos y changed Cot to reciprical --------sin y (sin y tany + cosy) sin y cos y common demonator --------siny (sin y tany + cos...
  3. P

    Find all solutions to Sin 2x = 2Tan 2x

    Is this correct?? Hello All I need to find all solutions to the following did i do it correct? Sin 2x = 2Tan 2x 2Sinx Cosx = 2(2Tanx / 1-Tan^2x) Sinx Cosx = (2(Sinx / Cosx)/(cos^2x-Sin^2x / Cos^2x)) Sinx Cosx = 2(Sinx / Cosx) X (Cos^2x / cos^2x-Sin^2x) Cosx = 2 (Cosx /...
  4. M

    Solving 3x Cos = 2x Sin: A Struggling Student's Guide

    solve for cos 3x=sin 2x using complementary angles and all i got alpha=2x. The thing is, if i got alpha 2x from sin inverse, the general formula would be \theta= n \pi + (-1)^n \alpha i get something like, so,...the problem is that i will have x in the general formuala...
  5. T

    Calculate sin and cos using complex numbers

    How can I calculate cos 72° and sin 72° using complex numbers, and without the use of a calculator? I noticed that 5*72° = 360° so (cos 72° + i*sin 72°)^5 = 1. But, I don't quite know how to go from there.. :shy:
  6. M

    What is sin x when x tends to infinity?

    This question popped up in my head. What is sin x when x tends to infinity? Since sine is a preiodic functions which repeats itself, is the answer 1, -1 or 0 or something else altogether?
  7. M

    What is the Derivative of cos(sin(x)) and Why is it Different from -sin(sin(x))?

    Hi I'm new here, great forum! On another thread that I can't find I found a message from jamesrc about differentiating cos of sinx that says: df(g(x))/dx = df(g)/dg * dg(x)/dx by the chain rule, this part I get and I thank james for the help the thing that confuses me is why df(g)/dg =...
  8. T

    Sin harmonic components are used in sound synthesis ?

    pyschoacoustically is it important wether cos or sin harmonic components are used in sound synthesis ?
  9. T

    Cos and Sin Components in Sound Synthesis

    cos and sin cont... Hi thanks for the help guys, I know this is more physics related but psychacoustically is it important wether cos or sin harmonic compoments are used in sound synthesis.
  10. V

    Calculating Supremum of sin n for Positive Integers

    I've got a question in analysis: How to calculate the supremum of sin n for positive integers n? I have tried hard but still cannot figure out it. Thanks very much to answer my question in advance! :smile:
  11. T

    Difference between Cos and sin

    Can anyone tell me the difference btween cos and sin, and tell me when creating waveform why the sin function creates a sawtooth appearance and the cos function does. Any help would be appreiciated. :!) :!)
  12. maverick280857

    Prove that sin 1 > cos ( sin 1 )

    Hi This is a fairly straightforward problem but I want to do it using calculus. Here goes: Prove that \sin 1 > \cos(\sin 1). This is what I've done (I've hardly done much): Let f(x) = \sin(\cos(\sin x) - \cos(\sin(\cos(x))). I also have to show that f(x) = 0 has exactly one solution...
  13. R

    What Is the Y-Axis Scale That Transforms Sine Waves into Straight Lines?

    What would you call the scale on the Y axis that would plot a sine or cosine wave as a straight lined saw tooth pattern? Is such a graphing style in use and does it have a name? RB
  14. JamesU

    Mastering Math: Understanding Sin and Cos for 7th Graders

    I'm a 7th grade student, but I study more advanced topics. I'm learning about mechanics, but it asks for sin and cos(cosin). I don't know too much about sin and cos, so I was wondering if anyone could explain it. :redface:
  15. V

    How to setup an integral in spherical coordinates for the volume of p = 2 sin O(theta

    Here is the problem: Find the volume of the region enclosed by the spherical coordinate surface \rho = 2 \sin\theta, using spherical coodinates for the limits of the integral. Here is what I have: I don't know if this is right, but here it is...
  16. J

    What identity should I substitute for the integral of sin^4(x)*cos^4(x)?

    can't figure this problem out for the life of me. the intergral of: sin^4(x)*cos^4(x) any help as to what idenity i should sub in?
  17. T

    What is the solution for this integral?

    Hi, I've been having troubles solving this integral: \int \frac{\sin x.\cos x}{\sin^4 x + x.\cos^4 x} dx Here's how I tried it: t = \cos x dt = - \sin x dx dx = \frac{dt}{-\sin x} x = \arccos t dx = -\frac{1}{\sqrt{1-t^2}} dt -\frac{1}{\sin...
  18. B

    Proving the Limit of Sin x/x Using Squeeze Theorem

    I've been looking at what I'm pretty sure is a standard result but I can't prove it. So can someone please help me out? \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{x} = 1 I think that it can be done using the squeeze theorem but I can't get to the answer. I started with - 1 \le...
  19. N

    Finding Sin r from 1.52 and 20 Degrees

    so my given is 1.52 20degrees = 1.10 sin r im trying to find sin r which comes out to 18.9 degrees but I am not sure how find that, can somebody help me out please? so you do 1.10/1.52 do you divide that into sin 20?
  20. A

    Check this for me involving sin theta

    Check this for me please involving sin theta For sin theta= -0.4321, 0<=theta<=2pi QUESTIONS a) How many solutions are possible? b)In which quadrants would you find the solutions? c)Determine the reference angle for this equation to the nearest degree. d) Determine all the solutions...
  21. 3

    Understanding the Relationship Between Sin and Cos in a Trigonometric Equation

    Given that n = Π[2 – 2cos(kπ/ n)] ... (where Π is the product sign , from k = 1 to n-1 ) as cos2@ = 1 – 2(sin@)^2 then 2 – 2cos(kπ/ n) = 4[sin(kπ/ 2n)]^2 , for k = 1 , 2 , 3 , … n-1 then n = Π[4[sin(kπ/ 2n)]^2] = [4^(n-1)] Π[sin(kπ/ 2n)]^2 but the book then said...
  22. P

    Exploring the Concept of Sin: Questions and Stories

    Have posted this in the philosophical section, but would be interesting to see replies from here, in a true conroversial style. the questions are: Does sin exist? What is your understanding of sin? Is sin the same as the concept of wrong? Where did your understanding of right and wrong...
  23. P

    Exploring the Concept of Sin: Questions to Stimulate Answers

    hi there, just some questions to stimulate answers, looking for allll different types of responses, so- go ahead and answer! Does sin exist? What is your understanding of sin? Is sin the same as the concept of wrong? Where did your understanding of right and wrong come from? Are the seven...
  24. M

    How can I find all w in C such that cos(z + w) = cos z for all z in C?

    Hi, How would I do the following: Find all w in C, such that cos(z + w) = cos z, for all z in C. Of course I would need to use the identity cos z = (e^iz +e^-iz)/2, but I have trouble finding w for all z. Thank you
  25. E

    Exploring the Limit of sin 1/x as x→0

    Either I can't find the correct la text or I'm doing it wrong but here goes: for a limit where x-->0 for sin 1/x Am I just supposed to recognize that as x goes to zero from the left that it goes to negative infinity and as x goes to zero from the right it goes to positive infinity? What...
  26. A

    Can you evaluate sin(-15 degrees) without using a special triangle?

    How do u evaluate \sin \frac {-\pi} {12} ? I converted the radian into degrees and got -15 degrees which is the same as 345 degrees. I made a circle with a cartesian plane and then sketched the angle it is in the 4th quadrant where sin is negative, but how do I evaluate? There is no...
  27. A

    Sin cos problem finding exact value

    sin cos problem finding exact value... I have to find the exact value of : \frac {\sin^2 45 degrees + \cos ^2 45 degrees} {\sin 60 degrees \cos 30 degrees} The squares are throwing me off , without them I got \frac {\frac {1} {sqrt2} + \frac {1} {sqrt2}} {3/2} what do I do with the...
  28. K

    Solving 10 Sin x = -x: Tips & Ideas

    10 sin x = -x can anyone give me tips how to solve this equation? i run out of ideas even to transform this equation to another form.. sigh sigh thanks...
  29. tony873004

    What is the difference between arcsin and inverse sin?

    What's the difference between arcsin and inverse sin? arccos and inverse cos? arctan and inverse tan?
  30. M

    I dont understand how antiderviative of 2 sin (2x) could be -cos(2x)

    i don't understand how the antiderviative of 2 sin (2x) could be -cos(2x), what happens to the 2? also how can the antiderivative of 5e^(5t) be e^(5t)?
  31. P

    How did mathematicans define sin?

    How did mathematican define sin A ( A >90 degree) as y/r? Are there any proofs to sin 150 = sin 30 >? The proof looks like, sin (180-A)= sin A, how can I get the geometry proof of this ? Anyone can help me ?
  32. M

    Cos(45 - v) = sin (v + 45) for all angles v?

    How can I prove that cos(45 - v) = sin (v + 45) for all angles v? :rolleyes:
  33. X

    Questioning the Limit of Sin x/|x| as x Approaches 0

    Hello all, I have a question that got me stumped. lim Sin x/|x| x->0 The above limit. Does it exist or not? If yes why, and if no why not. Any help would be greatly appreciated :-) Thanks, Xargon
  34. H

    Proving e^ix = cos x + i sin x

    How can I proof the identity e^ix = cos x + i sin x?
  35. M

    Finding Four Angles Using the Cosine Double Angle Formula

    Can someone please help me with this one? cos2x = 2 cos x sin x I need to find 4 angles :rolleyes:
  36. H

    Can the Numerical Value of Sin or Cos be Derived Without a Calculator?

    Assume you are given tan (pi/6). This means sin (pi/6)/cos (pi/6). But my question is, if you are given sin (pi/6) or cos (pi/6), is it possible to derive the numerical value without using calculator? -Thank you in advance.
  37. 4

    Trigonometry sin cos tan Question

    How do I do this? Thanks.
  38. S

    The Signs of Trigonometric Functions in Quadrant I and II

    I don't understand how they figure these problems out. Give the quadrant in which each of the following points are located, and determine which of the functions are postive and which are negative. (4, 3) Quadrant I; SIN +; COS +; TAN +; CSC +; SEC +; COT +; I understand that I think...
  39. C

    Math help: Solving trigonometric integral \int sin^2(4x)cos^{10}(4x)dx

    \int sin^3(4x)cos^{10}(4x) dx ok i know that i need to borrow the a sin, cause the sin has an odd power \int sin^2(4x)cos^{10}(4x) sin(4x)dx ok used one of the trig ids. on sin^2(4x) = \int (1-cos^2(4x)) * cos^{10}(4x) * sin(4x) dx =\int cos^{10}(4x)*sin(4x)dx - \int...
  40. M

    Voltage the wave form is a sin or a triangle in a dipole antenna

    Hi, If my input voltage the wave form is a sin or a triangle in a dipole antenna, what is the difference between these two wave forms? Thanks, Mica
  41. H

    Approximations for e^x, sin and cos

    I had a question on a math test which said that you should find an approximation for e^x which is very good for x \approx 0 . First I declared the function f(x) = e^x . We have the interesting thing that f(x) = f'(x) = f''(x) = f'''(x) \ldots \ \forall x . And because of this we have f(0)...
  42. M

    Differentiation of sin and cos

    i can't work out how to do this question, i have the answer, i just don't know how to get it Q. differentiate y = sin (cos x) A. - cos (cos) sin x If anyone could show me the solution, it would be greatly appreciated.
  43. A

    How Do You Calculate Fourier Series Coefficients for f(t) = sin(pi*t)?

    I am having trouble finding the An and Bn coefficients for the Fourier series f(t) = sin (pi*t) from 0<t<1, period 1 Please help! Thank you!
  44. M

    How Do I Integrate x * sin(pi*x/a) * sin(2pi*x/a)?

    As a minor step in a quantum mechanics problem I need to integrate x * sin(pi*x/a) * sin (2pi*x/a) over the interval 0 to a. I have had no luck and can't find it in my tables. Do I have to convert it to exponentials and integrate all those terms? I tried using sin 2y = 2siny cosy to...
  45. E

    Do you consider masturbation a sin?

    All those who think so raise your hand... well, that is after you wash it. eNtRopY
  46. STAii

    Approximating Sin() Graph: Discussion & Equation

    Greetings ! The other day i was fooling around a little with equations, i came up with an equation that (when graphed) look very similar to the graph of y=Sin() . Tell me what you think, and if anyone cares to know how i came up with it, i will tell. y = -1[ x/&pi; ]((-4x2/&pi;2) +...
  47. frankR

    I used Sin instead of Cos for a triangle.

    I just spent the last half hour trying to find my error in a problem. I checked my physics, my calculations, everything looked fine. It ended up being the simplest mistake I could make. I used Sin instead of Cos for a triangle. What a waste of time, it's the simplest mistakes you have to watch...
  48. D

    What is considered a sin and immoral behavior?

    ok people here is a little test moral charactor, reply to this thread with a list of things you consider to be sins / im-moral. and we'll discuss them. [?]
  49. E

    Sin of doing evil or the sin of not preventing evil

    i wonder..which is the greater sin: the sin of doing evil or the sin of not preventing evil?
  50. K

    What are Sin hx, Cos hx, Tan hx in Mathematics?

    sin hx, cos hx, tan h x... What are they? What does the "h" mean here? Any explanations or websites would be appreciated. :smile:
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