# Sin Definition and 17 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. ### 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...
2. ### 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...
3. ### 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))...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### Mass-Spring System Equation

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...
8. ### 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...
9. ### Separate a variable

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.
10. ### 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 Equations The...
11. ### How to know cos sin tan

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.
12. ### 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...
13. ### Diffraction Grating Problem ?

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...
14. ### 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...
15. ### Integral of sin and cos

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.
16. ### [Fourier transform] Convolution product with sin and cos

I'm asked to transform y(t) = x(t)*x(t) (where * is the convolution product) and x(t)= sinc(t)cos(2π10t) ( sinc(t)= sin(πt)/(πt) ). The attempt at a solution Clearly everything is simple if you know X(f), because y(t)=InverseFourier{ X(f)2 }. The problem is that I can't find X(f). By the way...
17. ### Is there an equivalent of cosx=1-(x^2/2) for the sin function

Hi, i was just wondering since cosx=1-(x^2/2) is there a similar formatted formula for sinx?? much appreciated :) :)