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. W

    Converting from sin to cos appropriately with phasors

    My transmissions line class often features problems where the voltage is expressed as a sin, not a cos. Obviously a phase shift of pi/2 is sufficient to convert between the two. However, I have trouble understanding when adding pi/2 is appropriate as opposed to subtracting pi/2. As per my...
  2. L

    Calculate the limit cos(x)/sin(x) when x approaches 0

    Hi, I need to check whether the limit of the following function exists or not I have now proceeded as follows to look at the right-sided and left-sided limit i.e. ##\displaystyle{\lim_{x \to 0^{+}}}## and ##\displaystyle{\lim_{x \to 0^{-}}}## To do this, I drew up a list in which I move from...
  3. thegoose

    The biomechanics of elbow extension

    𝐹𝑃𝑥 = 93.6650N sin (85 − 90) + 28.11N sin(180 − 85 − 79) Fpx= -8.16344N +7.74816N 𝐹𝑃𝑥 = -0.4154 N←
  4. brotherbobby

    Proving a trigonometric identity with ##\sin^4## s and ##\cos^4## s

    Problem statement : Let me copy and paste the problem as it appears in the text to the right. Attempt : Let me copy and paste my attempt. I couldn't go far, as you will see. I couldn't progress from here. The powers of the ##\sin## and the ##\cos## are both what we want (##8##), but the...
  5. R

    How to find out the sin value from cos

    First off sorry if something doesn't make sense, english is not my native language. I know i should start with sin2 α + cos2 = 1, but ant really continue from it. i am being confused by cos α = √5/3 since i know it isn't found in normal trig tables. So my problem is how to find out values of...
  6. karush

    MHB 5.2.1 vol of sin x^2 ; 0\le x \le \dfrac{\pi}{2}

    volume of the solid $y=\sin (x^2)\quad 0\le x \le \dfrac{\pi}{2}$ $\displaystyle \int_0^{\pi/2}\sin (x^2)\ dx$ ok think this should be area not volume but hope my int is set up ok
  7. S

    Using the sin function for a problem with a frictionless pulley and an incline

    To find the tension in the rope connecting 6.0 kg block and 4.0 kg block we do 6.0 kg = m1, 4.0 kg = m2, 9.0 kg = M (m_2 + m_1)a - Ma = Mg - m_2 gsin\theta - m_1 gsin\theta Why do we use sin in these equations and not cos?
  8. R

    Show that a projectile lands at a distance ##R = \frac{2v_0^2 sin \theta cos(\theta + \phi)}{g cos^2 \phi}##

    ##V_x = V_0 cos \theta ## ##x = V_0 cos \theta t## ##V_y = V_0 cos \theta ## ##y = V_0 cos \theta t## ##F_x = m\ddot{x}## ##-mgsin \phi = m\ddot{x}## ##\dot{x} = -gtsin\phi + V_x## ##x = -\frac{1}{2} gt^2 sin \phi + V_x t## ##x = -\frac{1}{2} gt^2 sin \phi + v_0 cos\theta t## ##F_y =...
  9. F

    I How do I do this calculation involving the SIN function?

    Hi, I am new here and hope I have posted my thread in the right forum. I have the following SIN function in Excel: =1*(SIN(2*PI()*1,6667*0,45)) The result is -1. That is what I want, so no problem. But what I want is a function that calculates the Time t value, in this example the value 0.45...
  10. brotherbobby

    Trigonometric equation of two sines

    Given : The equation ##\sin m\theta + \sin n\theta = 0##. Attempt : Using the formula for ##\text{sin C + sin D}## (see Relevant Equation 3 above), the given equation simplifies to \begin{equation*} 2 \sin \frac{(m+n)\theta}{2} \cos \frac{(m-n)\theta}{2} = 0 \end{equation*} This implies the...
  11. karush

    MHB Act.trig.02 sin theta >= 1

    For $-\dfrac{\pi}{2}\le \theta \le \dfrac{\pi}{2} \quad |\sin{\theta}\ge 1|$ is true for all and only the values of $\theta$ in which of the following sets $a.\ \left\{-\dfrac{\pi}{2},\dfrac{\pi}{2}\right\} \quad b.\ \left\{\dfrac{\pi}{2}\right\} \quad c.\ \left\{\theta | -\dfrac{\pi}{2}< \theta...
  12. nuclearfireball_42

    Can I determine the phase angle of this equation by using the sin function?

    I've got the answer for (a). It's k = 0.78 N/m. I'm having problems with (b). I know that the equation of displacement in this case should either be : x(t) = Asin(ωt + φ) or x(t) = Acos(ωt - φ) where A = amplitudeFrom what I understand, both the equation above should give the same result as...
  13. V

    Calculating the value of 1/{D^2+a^2} sin ax

  14. karush

    MHB 2.3.361 AP Calculus Exam of differentials of sin wave

    image due to graph, I tried to duplicate this sin wave on desmos but was not able to. so with sin and cos it just switches to back and forth for the derivatives so thot a this could be done just by observation but doesn't the graph move by the transformations well anyway?
  15. karush

    MHB 9.1.317 AP calculus exam multiple choice derivatives of sin wave

    ok just posted an image due to macros in the overleaf doc this of course looks like a sin or cos wave and flips back and forth by taking derivatives looks like a period of 12 and an amplitude of 3 so... but to start I was not able to duplicate this on desmos altho I think by observation alone...
  16. barryj

    How do I calculate the derivative of the inverse sin and inverse tan

    I calculated an expression for the derivative of the inverse tan but I did not use the identity as suggested. Why did I need to use this identity. Did I do the problem correctly? I got the correct answer. I tried to do the derivative of the inverse sin the same way. I used the same figure 1 on...
  17. bob45

    I Why do we use the sin x = x approximation for calculating waves on a rope?

    hi, when we try to find the speed of a wave on a rope v = (F/u)^1/2, we use the fact that if the angles are small then sin x = x. I understand the approximation but not WHY we use the approximation. We say delta(Theta) is small (and then amplitude is small) then ... . So the proof is only...
  18. karush

    MHB 33. Express sin 4x in terms of sin x and cos x

    Express function as a trigonometric function of x $$\sin(4x)$$ use $\sin2a=2\sin a\cos a$ then $$\sin4x=2\sin 2x\cos 2x$$ with $\cos(2x) = \cos^2(x)-\sin^2(x)$ replace again $$\sin 4x=4\sin x\cos x+\cos^2(x)-sin^2(x)$$ ok not real sure if this is what they are...
  19. Matt Benesi

    B Periodic smooth alternating series other than sin and cos

    1) Are there any periodic alternating series functions other than sine and cosine (and series derived from them, like the series for cos(a) * cos(b))? 2) What is the following series called when x is (0,1) and (1,2]? Quasiperiodic? Semi? \sum_{n=0}^\infty \, (-1)^n \...
  20. E

    MHB Evaluate cos 2(theta) and sin 2(theta)

    So my math professor gave us a study guide for the final but he's not aloud to give us the answers so I have no idea if my answers are correct or not. So if a few people could let me know what they got after trying this that would be great. If tan(theta) = -2[sqrt(2)], and theta is between 270...
  21. E

    MHB Find the sin angle between two 2d vectors

    Tomorrow is my math test and I'm going over the study guide: I have vector U=<1, 3> and vector V=<5, 2> It says let theta be the missing angle between the two vectors. What is the cos(theta) and sin(theta)? I already know how to find the missing angle for cos(theta) but we never covered how...
  22. Y

    Phase angle and Phase in Simple harmonic motion

    I'm a teacher at a Senior High School in Indonesia. I have two Senior High School physics books (Indonesian book) written about simple harmonic motion formula: y = A sin θ = A sin (ωt + θ0) = A sin 2πφ = A sin 2π (t/T + θ0/2π) phase angle = θ = ωt + θ0 phase of wave = φ = t/T + θ0/2π But I...
  23. F

    Graph the Cartesian equation: x = 2 sin t, y = 4 cos t

    Homework Statement Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction...
  24. anemone

    MHB Trigonometric inequality: sin (1/(n+1934))<1/1994

    Find the smallest natural number $n$ for which $\sin \left(\dfrac{1}{n+1934}\right)<\dfrac{1}{1994}$.
  25. Entertainment Unit

    Integral of 1/(a sin^2 x + b sin x cos x + c cos^2 x)

    Homework Statement If ##a \neq 0##, evaluate the integral $$\int \frac {dx} {a~\sin^2~x + b~\sin~x~\cos~x + c~\cos^2~x}$$ (Hint: Make the substitution ##u = \tan x## and consider separately the cases where ##b^2 - 4ac## is positive, zero, or negative.) The Attempt at a Solution $$\int \frac...
  26. G

    I Hertzian contact theory on sin and cosine plane

    Hello guys, i`m currently making simulation of 2 dimension rolling disk on elastic sin/cosine plane. I`m just wondering if the theory applicable.
  27. Mr Davis 97

    I Linear combination of sin and cos

    I have before me that ##\cos 2x + \sin 2x = \sqrt{2} \cos (2x - \pi / 4)##. Where does this expression on the right come from? I tried to look on the internet but I couldn't really articulate it well enough to find anything on it.
  28. M

    MHB Evaluate sin 6 without using a calculator?

    Evaluate sin 6 without using a calculator? How is this done? Unit circle?
  29. K

    Values of sin and cos (rad and deg)

    Homework Statement I am little confused. Value of used to be sin(0) = 0 = cos(1) sin(1) = 1 = cos(0) Homework EquationsThe Attempt at a Solution Now when I use google calculator I use rad or degree I do not get solid 1 and 0. for example sin(0)= 0 deg =0rad sin(1)= .841 deg = 0.017 rad...
  30. H

    How can I separate tan x and sin x in a limit problem?

    Homework Statement there is one question limx--->0tanx-sinx/x3 i actually tried to seprate tanx and sinx amd then i multiplied and divided by tan2x and sin2x so that i can make tan3x/x3and sin3x/x3 to be 1 and in the end sin2x canceled and i got the answer as -1 which is wrong what errror...
  31. Hawksteinman

    I Differentiation of sin function where's my mistake?

    I was thinking and came up with this. I know it's wrong but can't find the mistake :( dy/dx sin(x) = cos(x) dy/dx sin(kx) = kcos(kx) So dy/dx sin(3x) = 3cos(3x) Now let Y = 3x dy/dx sin(Y) = cos(Y) = cos(3x) 3cos(3x) = cos(3x) 3 = 1 Where is the mistake?
  32. E

    MHB Differential equation w/ cos and sin

    It would be wonderful if someone could please help with the following question as I don't even know where to begin y=y(x), where x^2 cos y + sin(3x-4y) =3Thank you :)
  33. L

    I Exploring the Limits of Trigonometry: 0 < sin x < x

    Given that 0 < sin x < x is true for 0 < x < π/2. From the above, can we conclude that 0 < sin (x/2) < x/2? How about 0 < sin (x/5) < x/5? Why? How about 0<sin 3x < 3x ? Why?
  34. Mr Davis 97

    I Small angle expansions for sin, cos, and tan

    From the Wikipedia article https://en.wikipedia.org/wiki/Small-angle_approximation, it says that they are "second-order approximations." What makes all three second order? Shouldn't sin and tan be first-order and cos be second-order?
  35. Jess Karakov

    Simplifying this derivative....

    Homework Statement Evaluate the derivative of the following function: f(w)= cos(sin^(-1)2w) Homework Equations Chain Rule The Attempt at a Solution I did just as the chain rule says where F'(w)= -[2sin(sin^(-1)2w)]/[sqrt(1-4w^(2)) but the book gave the answer as F'(w)=(-4w)/sqrt(1-4w^(2))...
  36. H

    Find theta given known cos and sin....

    Homework Statement Homework Equations cos 2theta = costheta^2 - sintheta^2 The Attempt at a Solution cos2theta = 1 2theta = 0, 2phi but i get wrong answer.. how is it?
  37. esha

    The graph of sin inverse (sin x) after the domain of (- pi/2, pi/2)

    the graph of sin inverse (sin x) between the domain of ( -pi/2,pi/2) is y = x. but after it crosses that domain of course the expression won't be the same anymore because sin inverse has its principle value as ( - pi/2, pi/2) due to sin x many to one natured function. now the way these...
  38. H

    B Definite integrals with +ve and -ve values

    I understand that if you have a function in which you want to determine the full (i.e. account for positive and negative values) integral you need to break down your limits into separate intervals accordingly. Is there any way in which you can avoid this or is it mathematically impossible? If...
  39. John Dalton

    B Understanding the Meaning of Sin, Cos, and Tan in Trigonometry

    I am eager to learn trigonometry. I have to be introduced to terms such as-sin,cos,tan,cosec etc. The internet"s explanation is going over my head. Can someone make them understand to me individually with the meaning of titha.(I cannot show its symbol , as it is not on the keyboard.) I will...
  40. F

    Solving for the Integral of sin (x^0.5)

    Homework Statement Integrate sin (x^0.5) Homework EquationsThe Attempt at a Solution I let u = sin (x^0.5) , du/dx = cos [(x)^0.5 ] ( 1/ (x)^0.5 ) , how to proceed ? [/B]
  41. Vital

    Graphs of sin and cos, how to set points for x values

    Homework Statement Hello! I am at the topic on graphing trigonometric functions. Exercises are rather easy at this point, but I have a problem deciphering how authors of the book choose points for x values. Please, take a look at few examples (including screen shots I attach), and, please...
  42. jlmccart03

    Finding frequency of an AC current sin wave?

    Homework Statement An AC current is given by I= 475 sin( 9.43 t), with I in milliamperes and t in milliseconds. Find the frequency. Homework Equations w = 2pi*f The Attempt at a Solution I got 9.43/2pi which is 1.5 Hz, but that is wrong. I honestly have no idea what to do to find the Hz.
  43. P

    Prove that lim x -> 0 sin (1/x) doesn't exist

    Homework Statement prove that \lim_{x\rightarrow 0} \sin \left( \frac{1}{x} \right) doesn't exist. Homework Equations \lim_{x\rightarrow0}\sin\left(\frac{1}{x}\right)=\lim_{u\rightarrow\infty}\sin u The Attempt at a Solution My strategy to solve this problem is to make u \rightarrow...
  44. R

    MHB If y = sin inverse (x square + 2x) find dy/dx

    if y = sin inverse (x square + 2x) find dy/dx
  45. solour

    Why does (-1)^n(sin(pi/n)) converge when (sin(p/n)) diverges

    Homework Statement I know that ∑n=1 to infinity (sin(p/n)) diverges due using comparison test with pi/n, despite it approaching 0 as n approaches infinity. However, an alternating series with (-1)^n*sin(pi/n) converges. Which does not make sense because it consists of two diverging functions...
  46. Mr Davis 97

    Deriving the sum of sin and cos formula

    Homework Statement Show that ##a \sin x + b\cos x = c \sin (x + \theta)##, where ##c = \sqrt{a^2 + b^2}## and ## \displaystyle \theta = \arctan (\frac{b}{a})## Homework EquationsThe Attempt at a Solution We see that ##c \sin (x + \theta) = c \cos \theta (\sin x) + x \sin \theta (\cos x)##. So...
  47. J

    Find y(t) for, x(t) = sin t and TF of a block is 1/(s+1)

    Homework Statement Find y(t) for, x(t) = sin t and TF of a block is 1/(s+1) Homework Equations Using Laplace of Input and then multiply laplace with TF to get O/P laplace and then doing Laplace Inverse The Attempt at a Solution Images are pasted below. Typed solution: Transfer Function...
  48. C

    How to calculate the gravity on a hill?

    The question is about a box with no movement standing on a hill. The hill has an angle of 25 degrees. The box has a mass of 40 kg. 1. Calculte the gravity This I still get: F= M x A = 40 x 9,81 = 3,9 x 10^2 The next question tough: 2. Calculate the component Fgravity,x off the gravity...
  49. binbagsss

    Sin inequality proof , ##0 \leq 2x/\pi \leq sin x##

    Homework Statement Homework EquationsThe Attempt at a Solution Hi How do I go about showing ##0 \leq \frac{2x}{\pi} \leq sin x ##? for ## 0 \leq x \leq \pi /2 ## I am completely stuck where to start. Many thanks. (I see it is a step in the proof of Jordan's lemma, but I'm not interested in...
  50. C

    Why does the Sin of 0.036 degrees approximately equal 2 pi?

    Homework Statement The formula for centripetal acceleration (Ac) is $$Ac = \frac {4π^2r} {T^2},$$ where r = radius and T = period of rotation Homework Equations The above formula can be rearranged as follows: $$Ac = \frac {2π} {T} × \frac {2π} {T} × \frac {r} {1},$$ $$= \frac {2π} {T} × \frac...
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