Cos Definition and 318 Threads

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...

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...

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...

From Dr. Leonard Susskind's Stanford Lecture: Quantum Entanglement, Lecture 4, he sets up a "given particle is spin up along n (arbitrary direction) and discusses : what is probability we measure up along another arbitrary m directionHe does all of the setup, - calculates the eigenvectors and...

Find amplitude, period, PS, VS. then graph. ok I think these are the plug ins we use $Y_{cos}=A\cos\left[\omega\left(x-\dfrac{x \phi}{\omega} \right)\right]+B \implies A\cos\left(\omega x-\phi\right)+B \implies T=\dfrac{2\pi}{\omega} \implies PS=\dfrac{\phi}{\omega}$ ok I wanted to do...

I tried this: X = cos(y) → y = arccos(x) for x E(-1,1) and y E (0,2) Then: There's a point I(Xi,Yi) in which: Cos(Xi) =Arccos(Xi) Then I said area1 (file: A1) A1 = ∫cosx dx definite in 0, Xi And A2 (file:A2): A2 = ∫cosy dy definite in 0, Yi And the overlapping area as A3 (file: A3): A3 = ∫Yi dx...

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...

I am attempting to find the sine representation of cos 2x by letting $$f(x) = \cos2x, x>0$$ and $$-\cos2x, x<0$$ Which is an odd function. Hence using $$b_n = \dfrac{2}{l} \int^\pi _0 f(x) \sin(\dfrac{n\pi x}{l})dx$$ I obtain $$b_n = \dfrac{2n}{\pi} \left( \dfrac{(-1)^n - 1}{4-n^2} \right)$$...

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 \...

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...

Homework Statement If x is a continuous variable which is uniformly distributed over the real line from x=0 to x -> infinity according to the distribution f (x) =exp(-4x) then the expectation value of cos 4x is? Answer is 1/2 Follow· 01 Request Homework Equations the expectation value of any...

r = np.arange(0,400,0.1) t = np.cos(r)+10 plt.plot(r,t) How can I use the range of the cos function to look like this

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...

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...

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.

cos 6x=(1/2)

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...

Homework Statement So in an AC circuit with inductance, I found I = (-ε_{max} cos(ωt)) / ωL I want to rewrite this as a sine function.Homework EquationsThe Attempt at a Solution I can ignore ε_{max} / ωL and work with -cos(ωt) I set ωt = θ I know cos(θ) = sin(θ+pi/2) so -cosθ =...

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 :)

This is of course just a silly exercise on a calculator, but it is intriguing that when operating in either degrees or "grad", hitting the cosine button will converge incredibly fast, whereas in radians it is a lot slower. Anybody have a good idea why?

Homework Statement In a article I have found this transformation (exp to bessel function) . I have two questions. Homework EquationsThe Attempt at a Solution a)where did the Cos go after setting n=1 and n=-1 ? in the third equations ( it is equal to -wmt-pi/2)? why?) b)how did the writer...

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?

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?

In the image below, why is the third line not \frac {ln(cosx)} {sinx}+c ? Wouldn't dividing by sinx be necessary to cancel out the extra -sinx that you get when taking the derivative of ln(cosx)? Also, wouldn't the negatives cancel?

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...

Homework Statement Hello! Last week I have came here for the help related to this problem. I am creating a new thread to describe the issue more precisely. I will be grateful for your help and explanation. I post the explanation for the book first accompanied by attached pictures, and below I...

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...

Homework Statement See below Homework EquationsThe Attempt at a Solution I am looking at a particular integral, and to get started, my text gives the indication that one should use partial fraction decomposition with ##\displaystyle \frac{\cos (ax)}{b^2 - x^2}##. Specifically, it says "then...

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...

Hello. Do you guys know if there is an identity related to this expression \cos(A+B)\cos(A+C) If so, can you help me how to derive it? I need it for the derivation of the formula from my circuits analysis course. Thanks.

find : (1)$ tan \,\, 15^o$ (2)$cos\,\,72^o$ (using geometry)

In kinetic theory, the number of molecules hitting a unit area of a surface per unit time with speeds between v and v + dv and angles between \theta and \theta + d \theta is found to be a function of sin(theta) and cos(theta). There will often be a practice problem asking to show that the...

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...

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...

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...

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...

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

Homework Statement I want to evaluate the following definite integral of the form, I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy where a, b, c, and d are constants, as part of a larger problem I am doing, Homework...

Find the volume of the solid generated by revolving the region enclosed by y= cos x and y = -cos x for [-pi/2, pi/2] about the line y=2pi.

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...

Prove that $\cos \dfrac{\pi}{7}$ is a root of the equation $8x^3-4x^2-4x+1=0$.

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...

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.

They ask for both $ \sum_{n=0}^{\infty} p^n Cos nx, also \: p^n Sin (nx) $ I'm thinking De Moivre so \sum_{n=0}^{\infty}p^n (e^{ix})^n = \sum_{n=0}^{\infty} p^n(Cos x + i Sin x)^n= \sum_{n=0}^{\infty} (pCos x + ip Sin x)^n I also tried a geometric series with a=1, $r=pe^{ix}$ But those...

Hi - going in circles about a step in an example, to find $ \sum_{n=0}^{N-1} Cos (nx) $ The book says we find \sum_{n=0}^{N-1} \left( e^{ix} \right)^n = \frac{1-e^{iNx}}{1-e^{ix}} , then take the real part. But I see $ \sum_{n=0}^{N-1} \left( e^{ix} \right)^n $ as a geometric series with...

Why 1 divided by cos(pi/4)=cos(-pi/4)? Is it wrong to say 1/cos(pi/4)=sec(pi/4)? Thanks

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?

Hey I need a second opinion to see if my formulas and calculations are correct. Also I need help with graphing this problem. My problem is to find amplitude, period, horizontal shift, vertical translation, step and then graph of: y= 2 - (1/3) cos ( πx + (3π/2) ) , -1/4 ≤ x ≤ 15/4 Using the...

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.

Homework Statement A student could either push or pull, at an angle of 30 degrees from the horizontal, a 40kg crate, where the coefficient of kinetic friction is .21. The crate is moved 18m. Calculate the minimum work for pushing and pulling. Homework Equations W=F•(change in)X•cos(angle in...