Theta Definition and 324 Threads

Homework Statement The speed of a projectile when it reaches its maximum height is 0.31 times its speed when it is at half its maximum height. What is the initial projection angle of the projectile? Homework Equations h=(Vi^2 * sin^2 θ) / 2g R=(Vi^2 * sin2θ) / g The Attempt at a Solution...

Homework Statement At 16:30 he writes (x sub 0)(cosine theta). Is x sub 0 the vertical component length of the position vector of the particle? When he labels x sub 0 a little while before, it looks as though x sub 0 is at the radial point along the x axis. How can you use x sub 0 cosine theta...

My professor, when doing trig substitution in lecture, always defines theta between certain intervals and when he takes the square root, he adds an absolute value bar to the trig function and then makes sure its positive through the interval. For practical purposes, is it necessary to go through...

Would this would the proper function, as described in the title of this thread, A = 1/2 x^2 \cos \frac{\theta}{2}? And suppose that the side x and the angle were changing with time, would the derivative, with respect to time, be \frac{dA}{dt} = x \cos \frac{\theta}{2} - 1/4 x^2 \sin...

Homework Statement What value(s) of θ will result in the block being accelerated 9.0m/s2 to the right? Homework Equations ƩFx = max N = mg - P sin(θ) The Attempt at a Solution P cos(θ) - μkN = max P cos(θ) - μk(mg - P sin(θ)) = max P cos(θ) + μk P sin(θ) = max + μkmg cos(θ) +...

Show that matrix A is invertible for all values of $$ \theta$$; then find $$A^{-1}$$ using $$A^{-1}= \frac{1}{det(A)}adj(A)$$ A = cos$$ \theta$$ -sin$$ \theta$$ 0 sin$$ \theta$$ cos$$ \theta$$ 0 0 0 1 ---------- By cofactoring along the 3rd row, I find det(A) = (1)*($$...

The problem says " Two forces of magnitudes 12 and 15 Newton are applied to a point and the tangesnt of the angle between them is -3/4. Find the resultant of the two forces and the measure of its angle of inclination on the first force. In the answer it says that the theta belongs to the...

What is the variable "theta of omega" in a series RL cct? Homework Statement Hi I'm not looking for a complete solution to this problem. My question concerns just one specific part of the solution to part A: why is tan θ(ω) = ωL/R? and what θ(ω) represent? how does it relate to the...

I am curious if I am setting this problem up right. Three forces act on the bracket. Determine the magnitdue and direction theta of F2 so that the resultant force is directed along the positive u axis and has a magnitude of 50lb...

Homework Statement How to find the values of theta that make tan theta > 1 true? The Attempt at a Solution From trial and error I can find the solution to be 45 < theta < 90, but I was wondering if there was a systematic process to determining these values. I also know according to...

Homework Statement A projectile is launched from the ground with an initial velocity of 140m/s at an angle of θ above the horizontal. (assume AR is negligible and the ground is level) The time of flight is 18.7seconds and its range is 1.98*10^3 show that the launch angle θ is approximately...

I haven't found a thread for latex tests, but I'm sure there's at least one of them. So feel free to move this post. ##\begin{array} \Phi (a, \theta ) = \sum _{l=0}^ \infty [A_l a^l + B_l a^{-(l+1)}] P_l (\cos \theta ) = V_a \\ \Phi (b, \theta ) = \sum _{l=0}^ \infty [A_l b^l + B_l b^{-(l+1)}]...

Homework Statement Solve main lobe of radio telescope if the power diagram is given as: P_{n}(\vartheta, \varphi)=sinc^{2}(a*sin\vartheta) Homework Equations Ω_{m}=\int\intP_{n} sin\vartheta d\varthetad\varphi The Attempt at a Solution Purely math question - but I have problem...

Homework Statement Here is a pastebin link to my question, it contains an algorithm, my trace of the algorithm, and my question.Homework Equations I am interested in the theta notation for the runtime of an algorithm The Attempt at a Solution Here is the link http://mathb.in/1202 My thoughts...

Homework Statement cos(theta) = -3/4, pi <= theta <= 2pi Homework Equations The Attempt at a Solution I forgot how to do this. How do I use the special triangles to do this question? Do I need to square the sqrt(3) / 2 one or something? Thanks.

Tensile stress given theta and force (I'm kinda desperate) Homework Statement Aluminum wire is lightweight. You can hang a piece of it nearly horizontally with very little tension. After having done so, you then hang a HEAVY (25 kg) block from the wire. The wire sags to make an angle of 12...

Homework Statement In a physics lab we were finding slope on semi-log graph paper, with the y (up) axis representing tension in Newtons, and the x (sideways) axis representing θ in radians. Sadly, the prof introduced the new concept of natural logs to me - I'd never heard of these until this...

Hi all, How do you go about solving this question as it says: Show that the matrix: | costheta sintheta 0 | B= | -sintheta costheta 0 | | 0 0 1 | is invertible for all values of theta [Hint. Show that det(B) is not...

Homework Statement A block of mass " lying on a ramp tilted at an angle  with the horizontal is connected to another block of mass # by a light string passing over a frictionless pulley as shown. If the block slides up the ramp with a constant velocity ), what is the...

Homework Statement Iv'e been given a graphed parabola with each x interval at 0.1000s. From this I need to find R, Tt, H, V0, a and θ. Homework Equations Tt= 2 (Vsinθ/g) R= (V2sin2θ)/g H=(Vsinθ)2)/2g The Attempt at a Solution From observing the graph I know: dx and dy at every 1/10...

Hi all, The following is part of a part, of an assignment for my MATLAB course for uni. For most of the ODE solvers in MATLAB you also have to be able to solve the question numerically - and this is the component of the question I'm doing here.. The equilibrium equation of an arch...

Homework Statement I need to write a function of theta in terms of a particular variable. I just can't seem to figure it out; the only solution I can come up with is when the aforementioned variable is equal to 0 or 1. I'm using Q to denote theta, and b is the variable. sin^3(Q)/cos(Q)=b^2...

Challenging Ramp and Pulley Problem Homework Statement Two blocks of masses 2m and m are connected by a weightless string over a frictionless, massless pulley, as shown in the figure. The coefficient of kinetic friction between the block and the incline is \mu. The system is in a uniform...

For $0<\theta < \frac{\pi}{2}$, find the solution(s) of $$\sum_{m=1}^{6}\csc \left\{ \theta +\frac{(m-1)\pi}{4}\right\}\csc \left\{ \theta +\frac{m\pi}{4}\right\}=4\sqrt{2}$$

Homework Statement The displacement vectors A and B, when added together, give the resultant vector R, so that R= A+B . Use the data in the drawing and the fact that = 29° to find the magnitude R of the resultant vector and the angle θ that it makes with the +x axis. I am unsure how to...

Consider a light ray emanating from the origin of a FLRW coordinate system in a homogeneous, isotropic universe. The initial velocity of that ray will have only x0 (t) and x1 (r) components. In papers I have seen it is assumed that its velocity will continue to have zero circumferential...

Homework Statement Consider a bead of mass m constrained to slide without friction along a rigid wire that rotates about the vertical at a fixed angle \theta with constant angular velocity \omega. Write down the Lagrangian in terms of z as the general coordinate. Find the equation of motion...

Working for a) Resolving upwards: 12cos(θ -90) - 8 = 0 cos(θ-90) = sinθ 12sinθ = 8 sinθ = 2/3 θ = 41.8 (3.sf) This makes no sense as theta is obviously obtuse, if I don't simplify to sinθ I get: cos(θ-90) = 2/3 θ = 48.2... + 90 = 138.2 (1.dp) Why does it not work if I...

Homework Statement We have the circle (x - 1)^2 + (y-2)^2 = 1. Find the boundaries of θ and r.Homework Equations x = h + rcosθ y = k + rsinθ The Attempt at a Solution This is a circle with its origin at (1,2) and a radius of 1 so r is between 0 and 1 and the circle lies in the first quadrant...

Hello everyone, I remember this from single-variable calculus: if f(x) = 2x, then df = 2dx, right? What if $f(r, \theta) = r\cos \theta$, how can I express $\partial f$ in terms of $r$ and $\theta$.? Thanks!

we know when theta is considered small enough, sin(theta) is approximately equal to theta. Ok, the question is what happens to theta dot(the time derivative of theta)?

In physics class, we always assumed both theta's. Can someone prove to me why the angle for gravity is the same as the angle of the inclined plane? I can clearly see that triangles could be created and visually they look similar, but obviously that isn't enough. Image is in the attachment...

Usually these problems are really simple for me, but this one is making me lose my mind: "An archer wishes to shoot an arrow at a target at eye level a distance of 49.0 m away. If the initial speed imparted to the arrow is 69.3 m/s, what angle should the arrow make with the horizontal as it is...

Homework Statement First off convert to z=(-i)1/3. Here is where I am stuck, how do I convert the above to this form: eiθ? I am mainly stuck because I don't know how to solve for theta. I know that θ = arctan(y/x) where y is the coefficient in front of i and x is the real value but in this...

shooting a cannon so that it explodes 10m off the ground above a target. The distance of the target is 1000m. Cannon is shot with a velocity of 10 m/s. Solve a) for θ and b)time in the air Homework Equations The Attempt at a Solution

Homework Statement Two ships are traveling parallel to each other in opposite directions with seed v1 and v2. One ship fire on the other. At what angle should the gun be aimed at the target ship in order to make a hit if the shot is fired at the instant when both vessels are on the straight...

Homework Statement A uniform rod is supported by two strings. The string on the left hand side is horizontal. The string on the right hand side is at 30 degrees with respect to a straight line going from the end of the bar to the ceiling. If you had a straight line going from the end of the...

Homework Statement I was given the following problem, but I am having a hard time interpreting what some parts mean. We're given the equation sinθ+b(1+cos^2(θ)+cos(θ))=0 Assume that this equation defines θ as a function, θ(b), of b near (0,0). Computer the Taylor polynomial of...

I'm looking at a Linear Algebra book that is using the greek letter θ for the zero vector. And the book has other bold letters, so it can't be that they simply could not make a bold zero. Has anyone seen such a usage before?

Homework Statement A block is resting on a wooden plank. On one end of the plank is a hinge so the other end my be lifted to create and angle θ with respect to the horizontal. The plank has a coefficient of static friction of μs. Using the sum of forces along the plank. Find the angle at which...

If f(x) is in theta of h(x) and g(x) is in theta of h(x), then is f(x)+g(x) in theta of h(x)? My initial thoughts on this are yes since the addition of the two functions shouldn't impact the value of the largest degree in both functions, as they would if they were multiplied, but I'm wondering...

If f(x) if big-theta of g(x), is it also always the case then that g(x) is big-theta of f(x)?

Homework Statement a) 2sin3x=sqrt(2). Find Theta. b) Cos4x=1/2. Find Theta Homework Equations The Attempt at a Solution a) sin3x=1/sqrt(2) Theta=pi/4. This is from the 45-45-90 triangle. Also Theta=3pi/4. How did they get this one? Can you guess it without looking at the...

Homework Statement Ship A is traveling due West towards a lighthouse at a speed of 15km/hr. Ship B is traveling due north away from the lighthouse at a speed of 10 km/hr. Let x be the distance between ship A and the lighthouse at time t, and let y be the distance between ship B and the light...

Homework Statement To show that \int_{0}^ \frac{\pi}{2}\sqrt{cos\theta}sin^3(\theta) d\theta = 8/21 The Attempt at a Solution The above expression was simplified as \int_{0}^ \frac{\pi}{2}\sqrt{cos\theta}sin^2(\theta) sin(\theta) d\theta \int_{0}^...

Given an equation for a line y=7x/3, how can i define it in mathematica using x,y and theta. I am eventually going to have to find the intersection of this line to a circle with the equation Circle[{0,9},5] as a function of theta. I thought maybe if i use the rule tan(θ) = y/x then id get...

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.

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...