Theta Definition and 324 Threads

Dear Forum, My goal is to rotate several points on a sphere by a theta and phi. For example, I have a sphere where the elevation is theta (90 to -90) and the azimuthal is phi (-180 to 180). I have the following points on the sphere: theta = [45 45 45 45] phi = [-180 90 90 180] This generate...

I am not sure what I am doing wrong but dot product of a and b =/= |a||b| when I am trying to calculate it. Theta = 0: dot product(a and b) = ax*bx + ay*by |a||b|= sqrt((ax^2+ay^2)*(ax^2 + by^2)) = sqrt((ax*bx)^2 + (ax*by)^2 + (ay*bx)^2 + (ay*by)^2) =/= ax*bx + ay*by What am I doing wrong?

This is a past paper question... find the solution here from ms ...wawawawawa...it took a little bit of my time because i was only thinking of taking limits...then realized that i was wrong as we have to remain with ##2θ##...i later realized that for small approximations, ##\cos θ≈1-\frac...

As the summary says we have ## f(x) = x^n - \theta \in \mathbb{Q}[x] ##. We will call the pth primitive root ## \omega ## and we denote ##[\mathbb{Q}(\omega) : \mathbb{Q}] = j##. We want to show that the Galois group is generated by ##\sigma, \tau## such that $$ \sigma^j = \tau^p = 1...

So in figure 4.8 the path difference between the two waves is d*sin(theta), then is the phase difference just (d*sin(theta)*2*pi)/lambda?

For the displacement, how do I figure out the angle theta between the points? And how does the speed at which the string retracts affect the centripetal force?

I am not sure if theta will be 60 degrees or 30 degrees in this case and Io is given.

So I get that: $$ \sin 2 \theta=-\frac{4}{5} $$ $$ \cos 2 \theta=-\frac{3}{5} $$ But what is the next step?

Here is my set up. Let t = theta for short tan(t) = 324/550 arctan(tan t) = arctan(324/550) t = arctan(324/550) Correct thus far? Note: What does "not to scale" mean in other words?

I can't solve ##\sin{\theta}\cos{\theta}=0,14## Thanks!

I have a vector field which is originallly written as $$ \mathbf A = \frac{\mu_0~n~I~r}{2} ~\hat \phi$$ and I translated it like this $$\mathbf A = 0 ~\hat{r},~~ \frac{\mu_0 ~n~I~r}{2} ~\hat{\phi} , ~~0 ~\hat{\theta}$$(##r## is the distance from origin, ##\phi## is azimuthal angle and ##\theta##...

Perhaps I should ask this question in the math section of these forums. But, I'm stumped and I don't think this equation is solvable? Find theta given all the other variables:

After impact VCos(alpha) will be normal to the inclined, now i calculated for theta by using [ Tan(theta) = vCos(alpha)/vSin(alpha),. Tan(theta)= Cot(alpha) ]. I don't know how to solve further to get value of theta, according to book thta = alpha.

Solving the relevant equation tan-1(30/7) = 76.865977693604 = 77 Just need confirmation or a correction since I am very new to physics in general

Hi, I am working on a Boltzmann equation question and I know that the solution I am looking for is that: log(nij/nji)=log(gij/gji)-Eij(eV)(5040/T) The only thing I don't understand is why log(e-Eij/kt) = θ = 5040/T From what I have read in textbooks, it is just a given, but I really want to...

Homework Statement A disk with a 0.4 m radius starts from rest and is given an angular acceleration α = (10θ2/3)rad/s2 , where θ is in radians. Determine the magnitude of the normal (centripetal and tangential components of a point P on the rim of the disk when t = 4s. Homework Equations α =...

Two highways intersect at a right angle. Two recording lights are located at points A and B, 200 meters and 300 meters away from the intersection on one of the highway. A car, C, approaching the intersection along the other highway, is being tracked by the two lights.Let θ be the angle ACB(see...

Homework Statement A certain football placekicker can kick the ball a distance d if she kicks it at 45°. a. Find an equation for the velocity of the kick. (You may use the range equation R = (V02/g)sin2θ.) b. Now imagine she kicks at a different angle θ. Show that a formula for the height y...

I'm trying to show that the theta term in the QCD Lagrangian, ##\alpha G^a_{\mu\nu} \widetilde{G^a_{\mu\nu}}##, can be written as a total derivative, where ##\begin{equation} G^a_{\mu\nu} = \partial_{\mu} G^a_{\nu} - \partial_{\nu}G^a_{\mu}-gf_{bca}G^b_{\mu}G^c_{\nu} \end{equation} ##...

1. the question is this: a projectile's speed at launch is four times its speed at the top of the trajectory. What is the launch angle? I am given no numerical values, but from my understanding gravity is a constant 9.8, and at the maximum height velocity should be equal to 0. 2.the equation...

Homework Statement Hello, I will post a picture below. An optical device consists of two glass blocks of different indices of refraction, arranged as shown in the picture. The refractive index from air to medium 1 is 1.2, and the refractive index from medium 1 to medium 2 is 1.25 If light is...

I have a very simple question. Let's consider the theta term of Lagrangian: $$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$ Investigate parity of this term: $$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$ $$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$ It is obvious. But what about...

What I've attempted to do is resolve vertically and horizontally: T1sin(30)+T2sinΘ+T2=9g T2cosΘ=T1cos30 After that... I'm completely stuck. Any help would be appreciated, I've spent so long on this I bet I'm just missing one simple thing. Thanks in advance

Homework Statement Homework EquationsThe Attempt at a Solution it seems like because theta 2 is independent, therefor, you can solve theta 3 by just using one equation from the system of equation? on a previous problem where its a 4 bar mechanism( which it didn't specify that theta 2 is...

Homework Statement Basic projectile motion if you throw from ground level, to obtain a max distance in the x you'd want to throw at a 45° angle right? So as your initial height increases, your throwing angle will decrease and my guess is as your initial velocity increases your angle increases...

Homework Statement Sino - ucos o =x Homework Equations N.A. The Attempt at a Solution I am asking if it's possible to make theta(o) the subject of formula in relation to some physics homework which I narrowed down to this but I don't know how to solve for theta, x is a known value but it's...

Homework Statement The motion of a particle is described in standard planepolar coordinates. Derive an expression for each of ##\frac{d\hat{r}}{d\theta}## and ##\frac{d\hat{\theta}}{d\theta}##, each in terms of one or both of ##\hat{r}## and ##\hat{\theta}## as necessary. Derive both results...

Homework Statement A skydiver is strapped to a rocket and shot into outer space. There is no air resistance so he is able to make his arms into a 45° angle with respect to his body and pretend they are "wings." To a stationary observer on the Moon (we will consider the Moon stationary for our...

Homework Statement A 3.0 kg block is released from the top of a rough ramp of length 2.0m and accelerates down the ramp at 1.6m/s^2. If a force of kinetic friction of 10 N acts on the block, what is the angle of the ramp. Homework Equations Fnet=ma ff=(mu? I don't have that symbol HAHA) muFn...

Homework Statement https://ibb.co/g6iKDQ Calculate the magnitude of the force on cables 1 and 2 in the figure below if θ_1 = 55° and θ_2 = 35°. (Round your answers to two decimal places.) Homework Equations Is my method incorrect or did I go wrong somewhere in my calculations?? The...

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?

Homework Statement A sector with central angle θ is cut from a circle of radius R = 6 inches, and the edges of the sector are brought together to form a cone. Find the magnitude of θ such that the volume of the cone is a maximum. Homework Equations Volume of a Cone = ⅓ * π * r2 * h Area of a...

I am working on planetary orbits in an ellipse where the sun is at the foci, not the centre of the ellipse. I need a formula that describes the 'Change of Distance by Change of Theta angle' where Distance represents the distance between a planet to the sun (Planet is on parameter, Sun is at...

Homework Statement P(-5,-2) is a terminal point of angle theta in standard position. State the exact values of all the trigonometric rations for theta. Homework Equations x^2+y^2=r^2 csc=1/sin sec=1/cos cot=1/tan The Attempt at a Solution

Homework Statement Question is provided The Attempt at a Solution The required solution is provided My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta Second question is how did they get rid of theta in the...

Why is ##\theta## a scalar whereas ##d\theta## a vector ?

Homework Statement 2bcosθ=2sinθ-1 where b is a constant Homework EquationsThe Attempt at a Solution I squared both sides, foiled, and changed the cosθ2 to a 1-sin2θ. Was told I need to solve a quadratic for sine? I don't see it.

Homework Statement For the theta series given by : ##\theta(t) = \sum\limits_{n\in Z} e^{2\pi i n^2 t} ## in 1-d there is the transformation formula: ##\theta(-1/4t)=\sqrt{-2it\theta(t)}## To prove this one uses the fact that this theta function is holomorphic and so by Riemann theorem it is...

The particular equation I would like to see solve is: ##\sin\theta\frac{d}{d\theta}(\sin\theta\frac{d\Theta}{d\theta})+\Theta(l(l+1)\sin\theta-m^2)## The solution for this equation is the following associated laguerre polynomial...

Homework Statement Rod of length b and mass m topples from vertical position at theta = 0. Calculate the reaction force f as a function of theta. What is the minimal and maximal values of f for theta between 0 and pi Homework Equations Third law?[/B]The Attempt at a Solution I never really...

##\theta(\tau, A) = \sum\limits_{\vec{x}\in Z^{m}} e^{\pi i A[x] \tau } ## ##=\sum\limits^{\infty}_{n=0} r_{A}(n)q^{n} ##, where ## r_{A} = No. [ \vec{x} \in Z^{m} ; A[\vec{x}] =n]## where ##A[x]= x^t A x ##, is the associated quadratic from to the matrix ##A##, where here ##A## is positive...

Homework Statement I have the Jacobi theta series: ##\theta^{m}(\tau) = \sum\limits^{\infty}_{n=0} r_{m}(\tau) q^{n} ##, where ##q^{n} = e^{2\pi i n \tau} ## and I want to show that ##\theta^{m}(\tau + 1) = \theta^{m}(\tau) ## (dont think its needed but) where ##r_{m} = ## number of ways of...

sin\theta 3/5

Mod note: Based on an attachment in a later post in this thread, the actual expression is ##(9 - 16\cos^2(\theta))^{3/2}## Homework Statement : https://www.physicsforums.com/posts/5610105/ Homework EquationsThe Attempt at a Solution my working is (9^1.5) - (16^1.5)[ (cos theta)^1.5 ] =...

Homework Statement A diffraction grating with 14100 lines per 2.54 cm (i.e., per in.) is used to view the visible spectrum from a Hydrogen gas excited by an electrical discharge. At what angle from the beam axis will the first order peak for the red photons with wavelength of 0.656 μm occur...

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

Homework Statement This problem asks for the angle on an inclined plane-- I have attached the problem below. Homework Equations fnet=ma The Attempt at a Solution I honestly have no idea what to do. I found the vector components for gravity and made a FBD for the box, but I can't really figure...

Homework Statement These two problems are inclined plane problems which I cannot figure out. The problems are attached in the image below. Homework Equations Fnet=ma The Attempt at a Solution I first broke down the gravity force into its x and y components. After that, I did this...

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...

Homework Statement A ball of mass m hangs vertically from a massless string experiencing a tension T. What force is required to pull the ball out to an angle theta from the vertical? 1) mgsin(theta)2) mgcos(theta)3) mgtan(theta)4) 2mg tan (theta)5) mg/cos (theta) Homework Equations no...