What is Theta: Definition and 333 Discussions

Pretty simple question. When we draw triangles or other pictures with angles, when do we mark the angles as alpha and when do we mark them as theta? Is there some kind of convention or is it just whatever is free in the equation? It makes sense to me to use alpha for the first angle then...

Homework Statement Use the Cauchy-Schwarz inequality to prove that for all real values of a, b, and theta (which ill denote as θ), (a cosθ + b sinθ)2 ≤ a2 + b2 Homework Equations so the Cauchy-Schwarz inequality is | < u,v>| ≤ ||u|| ||v|| The Attempt at a Solution I'm having...

How to find the initial velocity required for a projectile to be launched at an angle theta, with a distance 'd' and height 'h'. An expression is required. I am unable to find one using all three. Thanks in advance.

Homework Statement If a trajectory is shot at angle theta at a fixed projectile velocity of 50 m/s, what angle(s) could it be shot so that it just makes it over a wall 30 meters high, 220 meters down the path. Homework Equations d=1/2at^2+vt sinx*v=vertical component...

Hi, Currently, I need to read some reference about Integrable System, but I am stuck in Riemann Surface, genus, divisors, and Riemann Theta Functions. This makes me anxious. Is there introduction or pedagogical reference on this topic? I think I can spend some time read it during winter...

Homework Statement I saw in my calculus book that something along the lines of arcsec \frac{4}{\sqrt{pi}} = x was converted to arccos \frac{\sqrt{pi}}{4} = x. I understand that sec and cos are reciprocals, but I don't see why has to be flipped as well. Homework Equations cos (θ), sec (θ)...

[b]1. 95 m/s South + 435 m/s at 20 degrees North of East [b]2. Addition of vectors, and sin, cos, and tang. [b]3. For vector one I got 0 as my x component, and -95 as my y component. For vector 2 I got 408.8 m/s (x) and 148.8 m/s (y). cos(20)= x2/435 x2=408.8...

Can someone dummify what theta represents in Torque = rFsin(theta)? if my understanding of theta is correct for this problem theta would be 53 degrees. (See attached picture)

Hi, I'm reading through one of my books and it's explaining how a vector is eqaul to multiplying sin\phi and \Delta\vartheta. the way it's written in the text is as followed, |\Deltai| \approx (sin\phi)\Delta\vartheta I have never understood how things like this work. Could...

Homework Statement a crate with mass m rests on a horizontal floor. a woman pushes down at an angle of theta below the horizontalon the frace with a force F, the coefficient of kinetic friction is Uk. a) what magnitude of force F is required to keep the crate moving at a constant velocity...

Homework Statement Ok, so this is really basic and i could do it at the snap of a finger liek a year ago but it's completely escaped me. Maths is too much. This is a right angle triangle, with the right angle on angle C. Angles are marked A, B and C. Side CB = Adjacent, Side BA = Hyp and...

Hi all, I have some integrals involving Heaviside theta functions of non-trivial arguments, in particular \theta(1-x^2) and \theta(x^2-1). As x is a radial coordinate it's easy enough for me to break these up by hand, but it's cumbersome for me to implement in Mathematica and I can't work out...

Homework Statement i don't think this should be too hard, i just forget how to do it... so i have this problem, and I've got it down to this -490/sin2\theta + 2500cos\theta/sin\theta - 1800 = 0 if anyone can help...

Homework Statement using the equation a = g*sin(theta) where theta is in degrees how do i find g using the slope from a graph plotting acceleration versus theta? (i have acceleration on the y-axis versus theta on the x axis) Homework Equations a = g*sin(theta) where theta is in...

Homework Statement Find ∫ In(ζ) dθ , where ζ= cosθ and In(ζ) is the gegenbauer function of the first kind. The original problem is to find find ∫ sinθ *I//n(ζ) dθ where I//n= 2nd differential of In(ζ) with respect to ζ. Homework Equations d/dζ In(ζ)=-Pn-1(ζ), where Pn(ζ) is the legendre...

Help ! How can I find acute Angle theta?? How to find acute angle theta ,when tan 63 Degree = cot theta??Could anyone help me to find answer of this query.I need steps too as I am sooooo poor in mactematicuos:cry: .Final Answer of theta should be in degrees:smile: Thanks in advance:!)

Hello, I was wondering if the cosine of theta, in the work equation, related to the angle of the applied force?

Homework Statement This is a question from my test paper. If sec \theta=\frac{4xy}{(x+y)^2}, where x,y \in R, then (a)x,y \in R+ (b)x,y \in R- (c)x=y\neq0 (d)x\inR+, y\inR- Homework Equations The Attempt at a Solution I don't understand what i have to do and where should...

Homework Statement I made those illustrations up. :) We are asked to find the angle theta using the graphical method (Tail-to-Tip Method) From these examples, Vector A + Vector B + Vector C = Resultant Vector How to find angle theta of Resultant Vector? Homework Equations The Attempt...

let θ(x-x') be the function such that θ = 1 when x-x' > 0 and θ = 0 when x-x' < 0. Show that d/dx θ(x-x') = δ(x - x'). it is easy to show that d/dx θ(x-x') is 0 everywhere except at x = x'. To show that d/dx θ(x-x') is the dirac delta function i also need to show that the integral over the...

Find two solutions for Cosine theta = 1/2 for... [b]1. Find two solutions for Cosine theta = 1/2 for 0 degrees less than or equal to theta less than or equal to 360 degrees. Express answers in degrees and radians. Homework Equations [b]3. I know that Cosine theta = 1/2 gives you 60...

If p(x) is a probability distribution on the real number line, the "wrapped" distribution around the unit circle is: p_w(\theta)=\sum_{n=-\infty}^\infty p(\theta+2\pi n) which is periodic with period 2π. The (differential) entropy is: H=-\int_\Gamma p_w(\theta)\ln[p_w(\theta)]\,d\theta where...

Suppose I have a mass M_0 (here denoted with lowercase zero because of previous discussions on relativistic mass), and I have a gravitational field \phi which can under make a shift of 180^o between a negative plane and a positive plane. Assume also that the mass is considered as a charge...

Homework Statement From angles pi minus theta1 to pi plus theta1, what is the integral of cosine of 2 theta times d theta? Homework Equations The Attempt at a Solution When I evaluate this definite integral from pi minus theta1 to pi plus theta1, I get positive one half sine of...

2(exponential^theta)^2 - 10 = 6(exponential ^theta)

Which quadrant would this be? -3pi/2 < a < -pi I'm confused with this one. Would it be in the first or second quadrant? Thanks

question is (-2, 3pi) they want to find r>0 , -2pi< or equal to theta < 0 Isn't it just (-2 , pi) because you subtract 2pi from 3pi don't you? But the book says the answer is (2, -2pi) What in the world? The 2 in the actual correct answer is because of how polar coordinates are plotted it...

Homework Statement I'm trying to solve the 2-body problem analytically by following this book: http://books.google.com/books?id=imN_8IuZ8l8C&lpg=PR1&dq=David%20Betounes%20Differential%20equations&pg=PA60#v=onepage&q&f=false" (note: the book preview is not complete, but you can find pages 69-73...

non slip ball down an incline of theta! Homework Statement A uniform solid sphere rolls down an incline without slipping. If the linear acceleration of the center of mass of the sphere is 0.16g, then what is the angle the incline makes with the horizontal? Homework Equations F=ma...

Homework Statement Velocity final is 8 m/s velocity initial is 0m/s acceleration is -1.6m/s2 distance is 20m Mk is .2Homework Equations My teacher has given me sin(theta)=(square root) of 1-cos^2(theta) and cos(theta) = xThe Attempt at a Solution I'm a bit stuck, the part which I am up to is...

Homework Statement Tan \Theta = 12 / 5, sin\Theta<0Homework Equations Sin ^{2} \Theta+ Cos ^{2}\Theta = 1 The Attempt at a Solution Sin is less than 0 so... it should be somwhere in the II or III quadrant? What identities should I use to solve?

Homework Statement Vector A= 5.00 m (See the attached image for the graphical representation) Vector B=17.0m Vector C=15.0 m Homework Equations Pythagorean Theorem, Basic trigonometry The Attempt at a Solution Finding the magnitude of the resultant vector is not...

Homework Statement A uniform slender beam of mass 10 kg and length 1.2m is resting on a corner which is a knife-edge. The vertical wall on the left is smooth. What is the angle Θ for equilibrium? a=0.5m Homework Equations Can someone help me setup the formulas to solve this problem. I...

Homework Statement The ratio sin theta =-12/13 Homework Equations The Attempt at a Solution which comes out to according to my calcuations -0.9230, i then use 2nd sin function on my calculator and come up with -67.3 degrees this answer is legitimate but another way of writing...

Homework Statement In the equation ΔT = Pθ, P is power in Joules per second and ΔT is the temperature difference in °C. Use dimensional analysis to find the unit of θ. Hint, Joules has units of Force time distance. My question is: I don't understand what they mean by finding the unit of θ. Are...

Homework Statement This is what my professor is asking me to do: Show a table for when sin(theta) and theta have a percent difference of 1%, 5%, and 10%. (i.e. this table will have three columns)" You are to show this table (for all three quantities) such that the behavior leading slightly...

Homework Statement In lab, there was a string with a charged ball, and another charged ball moved closer to it. The ball's repelled and we had all sorts of data to calculate. I did a graph of the D vs 1/R^2 and the points fell almost right on. However, towards the end of that line, the...

Homework Statement If the cross product of vector v cross vector w = 3i + j + 4k, and the dot product of vector v dot vector w = 4, and theta is the angle between vector v and vector w, find tan(theta) and theta. Homework Equations vector c = |v||w| sin(theta) where vector c is the...

Homework Statement S = theta * radius I don't understand how they came up with this formula... can some one show me the proof how they derived this formula or can someone send me a link and I will just read it. Thank you. Homework Equations The Attempt at a Solution

Homework Statement Solve the equation 2cos^2\theta + 5cos\theta - 3 = 0\ for\ \frac{3\pi}{2}<\theta<5\pi Homework Equations quadratic equation, power reduction formula: cos^2\theta = \frac {1+cos2\theta}{2} The Attempt at a Solution First I tried using the quadratic...

Homework Statement Solve for Θ v2/RgsinΘ = sinΘ/cosΘ Homework Equations The Attempt at a Solution I did: (1) v2/RgsinΘ * (sinΘ) = sinΘ/cosΘ * (sinΘ) which gives me: (2) v2/Rg = sin2Θ/cosΘ then after converting some identities I get: (3) v2/Rg = tanΘsinΘ...

Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular separation of of the two light rays' second order maximum. -Need to find the absolute value of theta 650-theta 420 I know I need to use...

Homework Statement

Homework Statement A rocket is fired vertically into the air at a rate of 6 mi/min. An observer on the ground is located 4 miles from the launching pad. When the rocket is 3 miles high, how fast is the angle of elevation between the rocket and the observer changing? Be sure to specify units...

here is the problem. w= f*d*cos(theta). theta is changing so it involves integration. i know the answer its about 52. i know one solution for it but i have been trying to figure out how to solve it integrating with respect to theta. the way i know to solve it is let cos(theta)= x /...

1. What is the amplitude of the pendulum's motion, in meters? (see attached graph) Given: angular frequency=1.26rad/s 2. T=2pi(L/g)^.5; a=-w^2(x); s(t)=Acos(wt+phase); theta=s/L 3. I almost don't even know how to start.. The confusing part I believe is the graph. The max angle...

Homework Statement The graph below shows the component (Fcos(theta)) of the net force that acts on a 5.0 kg block as it moves along a flat horizontal surface. Find (a) the net work done on the block and (b) the final speed of the block if it starts from rest at s = 0. The graph shows...

Homework Statement Integrate. \int e^{2\theta}sin(9\theta) d\theta Homework Equations Integration by Parts \int udv = uv - \int vduThe Attempt at a Solution I started out with integration by parts (IPB). u = e^{2\theta} du = 2e^{2\theta} d\theta v = \frac{-1}{9}cos(9\theta) dv =...

I understand how to compare 2 functions and tell which bound they are in... but what I cannot comprehend is, given a single function... how do you write which bound it is in? Given a simple for loop like : for(int i = 0; i<n; i++) { for(int i = 0; i<j; i++) { System.out.println("Haha.")...

Homework Statement In the figure a fastidious worker pushes directly along the handle of a mop with a force F. (Note: For picture, imagine a worker standing in the second quadrant pushing the mop head into the origin) The handle is at an angle θ = 23.58° with the vertical, and 0.30 and 0.22...