# sine

1. ### On process, and on the derivatives of the powers of sine

Some background: A few months ago, I was on holiday in Prague. And I saw a nice clock there. Which led me to think about the equation of time. Which led me to think about y = x + e\,\sin y Which led me to think about \frac{e^k}{k!} \frac{\partial^{k-1}}{\partial x^{k-1}} [\sin^k x] Which...
2. ### Finding The Equation For An Unusual Sine Wave

Hello everyone. I made a post in another group trying to find the answer to a question about a particular sine wave, see link: https://math.stackexchange.com/questions/3383264/finding-an-expression-for-a-tricky-sine-wave Sadly despite offering a 'bounty' for it, I've not gotten very far...
3. ### Phasor Representation of sine wave

I don't understand why Sine wave should be represented as a phasor, that is, as a circle with a rotating vector. Why should it be rotating at angular speed (omega)? This is an additional item that confuses me. Suppose in the picture I am assuming it is moving at some speed; if it runs at twice...
4. ### Looking for something like Penner's Easing Functions, but for larger sets of data

Hey all, I work in CG, I'm a technical director (I help build tools that facilitate the work of animators in 3D animated productions, VFX and the like). We work with keyframes a lot, where we store the transforms of certain objects and parts of characters over time. These keys are represented...
5. ### Sine & Cosine Graphs- someone help me with this please

Here's the deal. I'm taking an integrated math class that I probably shouldn't, because it recommends taking Algebra 2 beforehand. I haven't taken Algebra 2. I was trying to avoid it, because, well I don't do algebra and this class isn't only about this stuff. This is just a section in it. But I...
6. ### Sine Rule: Can this be solved?

Sorry for the bother... Yeah, it is an elliptical problem. I know I am missing data to complete the use of the Sine Rule to solve it, but I am just wondering if knowing that C+A is already a known value might help. Just I cannot see it. There are other ways to solve it, I know, but I wanted...
7. ### What would you do next?

I want to break this down/ cancel stuff out: x = e + a + d \\ y = e + a \\ z = e + a/2 \\ c = e + d \\ \frac{v*\cos(c)*\sin(x)}{\sin(a)*\cos(z)}- \frac{u*\sin(c)*\sin(x)}{\sin(a)*\cos(z)}+ \frac{u*\sin(e)*\sin(y)}{\sin(a)*\cos(z)}- \frac{v*\cos(e)*\sin(y)}{\sin(a)*\cos(z)}...
8. ### Cancelling sums in fractions

Help me do the impossible, I'm looking at this: \frac{\sin(a+e)}{b}*\frac{u*\sin(e) - v*\sin(e)}{\sin(a)*\cos(e+a)+(1-\cos(a))*\cos(e+a)}-\frac{\cos(e+a)}{b}*\frac{u*\sin(e) - v*\cos(e)}{\sin(a)*\sin(a+e) + (1-\cos(a))*\cos(a+e)} As you can see, both sides of the subtraction are very...
9. ### Sine and Cosine to find area of surface

I am struggling with this one, finding the area of the land via the sine or cosine rule. I just don't see how I can go about it, I know I could use the formula for the area of a non-right angled triangle if I split it from B to D and make two triangles (Â½ ab sin C) However, I don't see how I...
10. ### Graph of sine function

- How would I graph 5- 3sin (2x) Thanks!
11. ### Galerkin Method Sine Series Expansion

I'm currently working on a 2-D Finite Difference code in MATLAB and am trying to check the approximations with the exact solution. Unfortunately I don't know how to employ the Galerkin Method to solve the given equation for exact results. Problem statement is attached. Any help is appreciated on...
12. ### An inequality involving hyperbolic sine functions

The following problem arised in my research work and has been challenging me for several days: Prove that for all $r\in (0,1)$ and for all $x>0$, we have $$\frac{\sinh(r(2-r)x)}{r(2-r)x} \bigg[ \frac{\sinh((1-r)x)}{(1-r)x} \bigg]^2 > \frac{\sinh(x)}{x} \frac{\sinh((1-r)^2x)}{(1-r)^2x}.$$...
13. ### Sin(2*theta) into 2*theta

Hey, I've gone a long way in this question, but I can't seem to get to the final answer. I've gotten up to sin(2*theta) = -1+(1/sqrt(2)). Doesn't seem like the double of a common angle and the question doesn't give any odd sines values. Any help would be really appreciated!
14. ### sine wave and sin function

Hello, What is difference in sin wave and sin function?
15. ### Sum of sine waves forming a circle

First of all, hi! IÂ´m a newbie to this forum. I use lots of maths for my games, so I decided to join the site. Now that I got that out of the way, IÂ´ll go straight to the point: Making a procedural roguelike with dynamic terrain. The ground is generated using a sum of sinewaves. Basically...
16. ### When is this sine function differentiable at all points?

The question is: For which values of a and b is the following function differentiable at all points? $$f(x)=\sin(|x^2+ax+b|)$$ I'm new to these kind of problems, so any help is deeply appreciated. Thanks in advance.
17. ### Fourier sine series

Find the Fourier sine series of function $f(x) = \left\{ \begin{array}{l} 0,0 \le x < \frac{1}{2} \\ (x - 1)\left( {x - \frac{1}{2}} \right),{\rm{ }}\frac{1}{2} \le x \le 1 \\ \end{array} \right.$
18. ### Is the sine or cosine inverse of improper fractions imaginary?

Greetings. I am Hariharan, a class 9 student. Of late, I've been working with Rene Descartes' method of geometric square root extraction (See SquareSquareRootConstruction). I tried to deduce an algebraic equation to find the square root of any number from this. Working further, I got some...
19. ### relationship between tangent, sine and cosine

Hi, how can I approach this problem? Also, could you tell me what results do you obtain?
20. ### amplitude-length of sine curve

I have an equation of the following form: y=Aâ‹…sin(Fâ‹…x) I want to create a sine function on a circle,somehow like the image of this link:http://bencrowder.net/images/2013/05/SineCircleTest-002.png. I want it to include 6 repeats of the function therefore if the length of the circle is...