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. L

    Solve for Sin teta=0 | Math Homework Help

    Homework Statement Homework EquationsThe Attempt at a Solution The first picture is the question The second picture is the marking scheme I have circled in yellow the problem I would like to know how sin teta = 0 Thank you
  2. B

    Trigonometric Substitution Problem w/ Sin Substitution

    Homework Statement ∫(√(64 - x^2)) / x dx I must solve this using a sin substitution. Homework Equations x = 8sinΘ dx = 8cosΘ dΘ Θ = arcsin(x/8) Pythagorean Identities The Attempt at a Solution (After substitution) = ∫8cosΘ * (√(64 - 64sin^2Θ)) / 8sinΘ dΘ = ∫(cosΘ * (√(64(1 - sin^2Θ))) /...
  3. C

    Curvature of r(t) = (3 sin t) i + (3 cos t) j + 4t k

    Homework Statement [/B] find the curvature of the vector valued function r(t) = 3sint i + 3cost j +4t k Homework EquationsThe Attempt at a Solution For the unit tangent vector , i got T(t) = (3cost i -3sint j +4k) / sqrt (9 ((sint)^2 ) + 9 ((cost)^2 ) + 4^2 ) = (3cost i -3sint j +4k) / 5 For...
  4. V

    Components of a force. When do I use cos or sin?

    Here is an example of a problem I am having trouble with. I need to find the i, j, k of A. I have no issues with finding the components for B, but A I just can't wrap my head around when to use cos or sin. Especially here with double projection. I know that A is : (-10 cos70 sin30, 10 cos70...
  5. C

    Value of Spring Stiffness k in Free Vibration of Mass-Spring System

    A mass-spring system is in free vibration after an initial excitation. There are no outside forces acting on the system. What is the value of the spring stiffness k (units of N/m; round your answer to a single decimal place)? Mass m = 0.6 kg Amplitude A = 0.4 Using this equation: z(t) = A sin...
  6. R

    B What is the derivation of this equation: d = t sin θ [ 1 - (n cosθ / n' cosθ)]

    Hi, Could someone please tell me how to derive this formula by using Wave Phenomenon d = t sin θ [ 1 - (n cosθ / n' cosθ)] I think some of it is derived using Brewster's Principle and the Refractive Index but I cannot tell how? Thanks.
  7. Hans Herland

    Find sin x expressed by a and b

    Homework Statement Firstly, sorry for the probably weird title. I have no idea how to title this problem, but hopefully my explanation is better. =) Given $$cos x = \frac {2\sqrt{ab}} {a + b},$$ where x is in the first quadrant and a + b ≠ 0, ab > 0. Calculate sin x expressed by a and b...
  8. karush

    MHB 242.8.2.8 int x sin (x/5) dx. IBP

    $\large{242.8.2.8}$ $\displaystyle I_8=\int(x)\sin{\left(\frac{x}{5}\right)} \, dx= 25\sin\left(\dfrac{x}{5}\right)-5\cos\left(\dfrac{x}{5}\right)x$ $$\begin{align} u&=\frac{x}{5} &5du&=dx &x&=5u \\ \end{align}\\ $$ thus $\displaystyle I_8=25\int u\sin{u} \, du$ IBP $$\begin{align} u_1&=u...
  9. A

    B How do you know if you need cos or sin?

    When solving a problem about shooting a cannon ball, why is the velocity in the x direction multiplied by cos and velocity in the y (vertical) direction multiplied by sin? like in the last example here...
  10. M

    MHB Find cos theta and tan theta using sin theta

    If sin \theta =\frac{4}{5} , find cos \theta and tan \theta Can you help me to solve. :) Many thanks :)
  11. shina

    How can I get involved in the scientific community at PF?

    Myself shivani and I have joined this site recently. I hope you all will cooperate with me
  12. U

    Simultaneous equation involving cos, sin

    Homework Statement i have solve a engineering problem until this part I'm stuck C cos 30 - 1.375 cosθ = 0 ----(1) C sin 30 + 1.375 sin θ = 15 ---(2) . i have 2 unknown C and θ, however the change to cos to sin or via versa make me lost because of my poor mathematic Homework Equations The...
  13. karush

    MHB Integrating by Parts: Solving a Sin x Problem

    \\text{w8.4.13 Integration by Parts} nmh{2000} $\displaystyle I=\int \sin\left({\sqrt{x}}\right) \ d{t} =2\sin\left({\sqrt{x}}\right) -2\sqrt{x}\cos\left({\sqrt{x}}\right)+C$ $\begin{align} \displaystyle u& = {\sin\left({\sqrt{x}}\right)} & dv&={1} \ dx \\ \\...
  14. N

    I Solve for the offset of two sin waves

    Hey all, how does one solve sin(ax + by + c) = sin(ix + jy + d) for d and c if you only know the difference between d and c? Any help appreciated, simply arcsin'ing both sides does not work as you get impossible answers in the exact example I had.
  15. I

    Find cscθ Given sec θ = -2, sin θ >0

    Homework Statement Find cscθ given sec θ = -2 sin θ >0 Homework Equations I do not know where to begin or what equations to use. The Attempt at a Solution I am assuming there is a typo in the question and that there should be a comma sec θ = -2, sin θ >0. If so I got csc θ = 2√3 / 3
  16. RoboNerd

    I Question on basic trig substitution with x = sin theta

    Say I have the integral of [ 1 / ( sqrt( 1 - x^2) ] * dx . Now I was told by many people in videos that I substitute x = sin theta, and this has me confused. Wouldn't I need to substitute x = cos theta instead? as x = cos theta on the unit circle instead of sin theta? Thanks in advance for...
  17. V

    B Couple geometry/trigonometry questions

    I am reading Gelfand's Trigonometry. In one of the questions he asks: "We know from geometry that a circle may be drawn through the three vertices of any triangle. Find the radius of such a circle if the sides of the triangle are 6,8, and 10." My first question is, I know that if the diameter...
  18. V

    Adjusting the Model: d = 12 sin (30(t-5)) + 14

    Homework Statement Modify the model d = 12 sin (30(t-5)) + 14 to match the new data which is as follows; maximum water depth is 22 m minimum is 6 m, and the first high tide occurs at 5:00am. Homework EquationsThe Attempt at a Solution The answer is y= 8 sin (30(t-2)) + 14 Ik it's 8 b/c...
  19. Ray9927

    Doubt about trigonometry Identities from sin α

    Hi all! I'm Ray and I'm new to this community, it's a pleasure! I'm trying to resolve a trigonometry exercise where I have to calculate the trigonometry Identities of a right triangle but in the specifications they don't show me any common data (hypotenuse or cathethus values), they just leave...
  20. Oaxaca

    Complex Conjugates with sin and cos

    I am rather new to the whole idea of complex conjugates and especially operators. I was trying to understand the solution to a problem I was doing, but the math is confusing me rather than the physics. In the last row of calculations, why does the sin change to a cos, and the d/dx change to...
  21. Z

    Separate Variable Homework: Solutions & Equations

    Homework Statement m1v1=m1v1'cosa+m1/2v2'cosB 0=m1v1'sina-(m1v2'sinB/2) m1v1^2=m1v1'^2+(m1v2'^2)/4 Homework Equations The solution in my book is v2'=2v1sqrt(3) The Attempt at a Solution I thought to separate v1' at the firts and put it at the second, but I don't know how to change sin and cos then.
  22. kostoglotov

    Need help understanding how these limits were evaluated

    Homework Statement Hi, the problem is imply to show the following \lim_{n\rightarrow \infty} 10^n e^{-t} \sinh{10^{-n}t} = \lim_{n\rightarrow \infty} 10^n e^{-t} \sin{10^{-n}t} = te^{-t} How can I do this? Just a hint or a first step would be great, thanks :) Homework EquationsThe Attempt...
  23. Ryaners

    Finding inverse of a Sin function (problem from Mooculus)

    I'm working through the problems in the Mooculus textbook as revision for Calculus I & there seems to be something wrong with how I'm manipulating the function to find its inverse in the following example. Homework Statement The height in meters of a person off the ground as they ride a Ferris...
  24. Taryn1

    MHB Sum or difference formula (sin, cos, and tan)

    So I'm supposed to find the exact values of the sine, cosine, and tangent of an angle by using a sum or difference formula ( i.e. sin(x+y)=sin(x)cos(y)+cos(x)sin(y) ), but this is the angle I was given: ${-13\pi}/{12}$. How do I use a sum or difference formula to get the sin, cos, and tan of that?
  25. S

    What Is the Exact Value of Sin 345.5 Degrees?

    Homework Statement Find the exact value of sin 345.5o Homework Equations Trigonometry Identities The Attempt at a Solution Don't know where to start. Tried sin 345.5o = - sin 14.5o but stuck. Also tried multiply 345.5 with positive integer to get sin 2θ or sin 3θ or sin 4θ but also stuck Thanks
  26. S

    Exact Value of Sin 65 Degrees: Trigonometry Identities for Finding the Solution

    Homework Statement Find the exact value of sin 65o Homework Equations Trigonometry Identities The Attempt at a Solution I tried using sin 3x = 3 sin x - 4 sin3x but ended with nasty algebra. sin (3 . 65o) = 3 sin 65 - 4 sin3 65o sin (195o) = 3 sin 65 - 4 sin3 65o sin (180o+15o) = 3 sin 65 -...
  27. saybrook1

    Alternative Derivation of sin integral

    Homework Statement Hi guys; I'm just dealing with Fourier series and they evaluate integrals such as ∫sin(nπx/L)dx from 0 to L as (L/nπ)[1-(-1)^n]. Can someone please tell me how to get to this conclusion or point me in the direction of a resource that will show me? Additionally I need to solve...
  28. T

    How Do You Integrate Complex Trigonometric Functions?

    Homework Statement (This is a part of the entire problem. I'm just struggling with going to the next step since it involves solving this integral.) Integrate: $$ \int \frac {1}{\sin \theta \sqrt {R^2\sin ^2 \theta - a^2} } d\theta $$ Homework Equations R and a are simply constants. Only $$...
  29. jpcyiu

    Is There a Trick to Remembering the Trigonometric Functions?

    hello everyone! I want to know how to verify cos sin tan I always feel confused when i am doing the physics exercises. are we always use cos when it is x-axis and use sin when it is y-axis?? I feel so confused.
  30. N

    Proving the Inequality: sin(x) < x for x > 0

    Hello all, I want to prove the following inequality. sin(x)<x for all x>0. Now I figured that I put a function f(x)=x-sin(x), and show that it is increasing for all x>0. But this alone doesn't prove it. I need to show we have inequality from the start. I can't show that lim f(x) as x->0 is...
  31. Emmanuel_Euler

    Finding sin and cos without using calculator

    Hi everyone. i think this is my last thread on PF:frown:! because i am too busy,anyway, 4 months ago i posted a thread named it finding cube roots without using calculator and now i want to know if there is a way or method to find sin and cos without using calculator. And thanks to all who...
  32. J

    Calc BC derivative problem with trig and double angle -- Help please

    Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx The Attempt at a Solution We're...
  33. B

    What is the Method to Calculate Sin β in a Triangle?

    How do you find the numerical value sin β for the triangle shown on below image? I can only find ##\tan β = \frac{AB}{BD} = \frac{2x}{3x} = \frac{2}{3} = 0.666666667## then ##β = \tan^{-1} 0.666666667 = 0.59°## then ##\sin β = \sin 0.59° = 0.0103## Is there another method to find the...
  34. J

    Confusion regarding cos or sin

    Homework Statement I have the solution and everything, I'm just confused why they use cos for Fy and sin for Fx ... Homework Equations I've always known Fx=Fcos and Fy=Fsin .. but now I am getting to different problems and it confuses me The Attempt at a Solution I read many posts and answers...
  35. terryds

    Given isosceles triangle, find sin (A-C)

    Homework Statement Triangle ABC have side AB = 10 cm, AC=BC = 13cm, so sin (A-C) is... 2. Homework Equations sin (A-C) = sin A cos C - cos A sin C The Attempt at a Solution I see that the triangle can be split into two right-angle triangles. But, sin (A-C) ?? How to get that?[/B]
  36. karush

    MHB How Do You Convert a Trigonometric Expression into a Sine Equation Form?

    $$-2 \sqrt{3}\cos\left({\theta}\right)+6\sin\left({\theta}\right) $$ Convert to $$A\sin\left({B\left[\theta-C\right]}\right)+D$$ I couldn't find an example how to do this coversion
  37. arpon

    What is the inverse function of x + sin x ?

    What is the inverse function of ##x+sin x## ?
  38. Ayso24

    A Quick "Lesson" on Physics and sin graphs

    Homework Statement Well instead of asking the entire question, I just would like some help getting started. What equations, or even some lesson plans/examples, are out there that can help me with finding things like velocity, distance moved, force, etc on something that moves along a sin...
  39. ognik

    MHB Find Roots of sin z: Solutions & Explanations

    Looking for someone to check my working & answers please. Problem is 'find all the zeros of sin z' A) sin z = sin(x+iy) = sin(x)cosh(y) + i cos(x)sinh(y) Roots are when sin(x)cosh(y) = 0 = cos(x)sinh(y) $If \: sinh(y)=0, then \: cosh(y)=1 \: (cosh^2 - sinh^2=1) $ $ \therefore sin(x) = 0...
  40. M

    Motivation of sin and cos functions

    Is there a way to motivate the sinus and cosinus functions by looking at their Taylor expansion? Or equivalently, is there a way to see that complex numbers adds their angles when multiplied without knowledge of sin and cos?
  41. T

    MHB How to find the answer sin 120.

    I was reading on a forum that $$sin120$$ is equal to$$ sin60$$. How is this? Shouldn't$$ sin120$$ equal $$sin60 + sin60$$?
  42. J

    Integrating acceleration sin wave

    This is a really basic calc/physics question.If acceleration is defined as Acc= Asin(w*t), and I integrate this to get velocity, I get Vel=(-A/w)*cos(w*t)+C. If the velocity at t=0 is 0, then C=A/w. If I then integrate the velocity to get the displacement, I get...
  43. Shahab Mirza

    What Angles Reveal Second Order Bright Fringes in Diffraction?

    Hi, 1. Homework Statement Q : A diffraction grating with 10000 lines per CM is illuminated by yellow light of wavelength 589 nm, At what angles is the 2nd order bright fringes seen ?Homework Equations From my textbook , I got this equation , d sin theta = m (λ) The Attempt at a Solution Ok so...
  44. M

    Eliminate Parameter with Sin and Cos

    x = 2 − π cos t y = 2t − π sin t −π ≤ t < π I understand how to eliminate parameter using sin^2 + cos^2 = 1. I can't figure out how to deal with the "2t" in the y equation, if you solve for sin(t) and square, you get ((2t-y)/π )^2 which leaves the parameter. Is there a way to get it into the...
  45. B

    Does the Identity Sin² x + Cos² x = 1 Apply to All Multiples of x?

    I know that ##\sin^2 x + cos^2 x = 1.## Is this mean that ##\sin^2 2x + \cos^2 2x = 1## or ##\sin^2 3x + \cos^2 3x = 1## or ##\sin^2 4x + \cos^2 4x = 1## and so on?
  46. S

    How to tell when to use Cos vs sin in physics

    Homework Statement The first problem was " A 50 N crate is pulled up a 5m inclined plan by a worker at constant velocity. If the plane is inclined at an angle of 37degrees to the horizontal and there exists a constant frictional force of 10N between the crate and the surface, what is the force...
  47. T

    Solving Triangles. My answer fluctuates from the real answer

    Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...
  48. A

    Time derivatives of sin and cos phi

    Homework Statement By using chain rule of differentiation, show that: $$ \frac{\mathrm{d} sin\phi }{\mathrm{d} t} = \dot{\phi} cos\phi , \frac{\mathrm{d} cos\phi }{\mathrm{d} t} = -\dot{\phi} sin\phi , $$ Homework EquationsThe Attempt at a Solution I got this right for a homework problem...
  49. blue_leaf77

    Proving the Stability of Sin and Cos through the FT Relation of Delta Function

    Starting from FT relation of delta function, I can write the followings: $$ \int_{-\infty}^{\infty} \cos{\alpha x} dx = 0 $$ $$ \int_{-\infty}^{\infty} \sin{\alpha x} dx = 0 $$ The question is how am I supposed to prove those equations, sin and cos are stable oscillating functions.
  50. M

    Infinite series of sin + cos both to the 2n power

    Homework Statement For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum. (ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations geometric series, [/B]The Attempt at a Solution First I have to show that the equation is convergent. Both cos(θ)...
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