# What is Theta: Definition and 333 Discussions

Theta (UK: , US: ; uppercase Θ or ϴ, lowercase θ or ϑ; Ancient Greek: θῆτα thē̂ta [tʰɛ̂ːta]; Modern: θήτα thī́ta [ˈθita]) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth . In the system of Greek numerals it has the value 9.

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1. ### Rotate Points on Sphere by Theta and Phi

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...
2. ### I Confused about dot product of a and b = |a||b| if theta = 0

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?
3. ### Show that ##2 {\cos \theta} +(1- \tan \theta)^2≈ 3 - 2\theta##

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...

24. ### Finding Tension and theta in a pulley system

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
25. ### Why is Theta 2 Independent in Solving for Theta 3 in a 4-Bar Mechanism?

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...
26. D

### Finding an expression for max distance in terms of theta

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...
27. T

### Can Trig Ratios Solve for Theta in a Physics Homework Problem?

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...
28. S

### Change in r-hat by change in theta

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...
29. ### Finding Angle Theta in Relativistic Skydiving Scenario

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...
30. B

### Dynamics ramp and friction. Finding angle?

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...
31. ### Force on 2 cables with weight attatched using Theta....

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...
32. ### Find theta given known cos and sin....

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?
33. ### Find the Magnitude of Theta to Maximize Volume of a Cone

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...
34. ### MHB Formula for Ellipse 'Change of Distance by Change of Theta'?

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...
35. ### State the exact values of all the trigonometric rations for theta.

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
36. ### Solving a Physics Problem: Sine vs. Cosine Theta

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...
37. ### B Confusion between ##\theta## and ##d\theta##

Why is ##\theta## a scalar whereas ##d\theta## a vector ?
38. ### Solving for Theta in 2bcosθ=2sinθ-1 Quadratic Equation

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.
39. ### Generalising theta transformation formula from 1-d to m-d

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...
40. ### A Solve DE for theta component (hydrogen WF)

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...
41. ### Rod is toppling. Find reaction force as a function of theta

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...
42. ### A Representation number via quad forms of theta quadratic form

##\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...
43. ### Jacobi Theta Function modularity translation quick q

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...
44. ### MHB Find the exact value of each of the remaining trigonometric functions of theta

sin\theta 3/5
45. ### Change (9-16cos theta) ^1.5 into another form

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 ] =...
46. ### How to find theta in a mutiple slit question

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...
47. ### 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 :)
48. ### What is the solution to this inclined plane problem?

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...
49. ### Inclined Plane Problem-- Solving for Theta

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...
50. ### 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...