Angles Definition and 892 Threads

In another thread, it was asked if we could use the angular deficit idea to determine curvature not in space, but in space-time. My idea to attempt to proceed along these lines would be to generalize the idea of angle, but I don't have anything that I feel I can point to. As a starting...

I am trying to diagonalize the following matrix: M = \left( \begin{array}{cccc} 0 & 0 & 0 & a \\ 0 & 0 & -a & 0 \\ 0 & -a & 0 & -A \\ a & 0 & -A & 0 \end{array} \right) a and A are themselves 2x2 symmetric matrices: a = \left( \begin{array}{cc} a_{11} & a_{12}\\ a_{12} & a_{22}...

Given that $PA,\,QB,\,RC$ are the altitudes of the acute triangle $PQR$ such that $9\vec{PA}+4\vec{QB}+7\vec{RC}=0$. Show that one of the angles of triangle $PQR$ is $60^{\circ}$.

Homework Statement Prove that if bonding-pair repulsions were maximized in CH3X, then the sum of the bond angles would be 450°. Homework Equations In a perfect tetrahedral molecule (e.g. methane), the sum of the bond angles is about 438 degrees (109.5° times 4). The Attempt at a...

Homework Statement Consider the geometric isomer of PBr2F3 with a Br-P-Br bond angle somewhat larger than 120 degrees. It is also true that for this isomer ... There are two sets of identical bond angles. Homework Equations PBr2F3 is trigonal bipyramidal (although distorted)...

In physics, when we draw a block on an incline, we know that the angles are the same see image: Incline angle = angle formed by Mg, M, F_2 I can't recall what geometry properties allows us to make this statement.

Problem statement: The Bragg angles of a certain reflection from copper is 47.75◦ at 20◦C but is 46.60◦ at 1000◦C. What is the coefficient of linear expansion of copper? (Note: the Bragg angle θ is half of the measured diffraction (deflection) angle 2θ). Attempt at solution: Using...

i know that question is a little basic but i have no one to ask. for this image i think that the angle between the horizontal and the normal force that the semi-cylinder exert on the bar is is α - 90° Original Image for this one i think that the angle between the horizontal and the...

Homework Statement got a vector F (105,300,140) magnitude: 347.3 it wants the angles, 3 of them with the axis x y z Homework Equations all my calculations has lead to the wrong answer, but the correct answer is (180-myanswer) why is that? The Attempt at a Solution...

Homework Statement From an alien spaceship Earth is in the direction (1, -8, -4) and Venus is in the direction (3, 12, 4). The average alien eye has a field of view of 5pi/6 radians. Without using arccos or calculating any exact angles, determine if the average one eyed alien on the spaceship...

Hello everyone. Can someone explain the relationship between the idea of a sine wave, and the idea of a sine angle? I'm getting into trig, and I hear both terms of sin tossed around, but they seem to be completely unrelated. What does the angle of the triangle have to do with a wave? Same...

Homework Statement What are the number of different bond angles for the isomer of F_{3}PCl_{2} with each chlorine equatorial? What about for the isomer of BrPF_{4} with the bromine axial? According to the key the the first molecule has 5 unique bond angles. Homework Equations Trigonal...

Kind of just a general question...I took a theoretical physics class last semester and we went through this whole book "Div, Grad, Curl, and All That Vector Calculus". Now I'm in an upper division E&M class and we're using Griffith's "Intro to Electrodynamics". In my 3rd semester of calculus and...

I just don't understand others way solving this problem to solve for the unknown magnitudes of the two vectors I have to sum up all of the components in x and y and set them equal zero and from there I'll get some systems of equation. I saw a method where they let the x-component of AB and BE...

Hello, I am using a very old textbook from 1895, Loney's Trigonometry, which poses the following problem: If the circumference of a circle be divided into 5 parts, which are in A.P., and if the greatest part be 6 times the least, find in radians the magnitudes of the angles that the parts...

[b]1. Homework Statement [/ In 3-D coordinate space, any two of the coordinate angles must … Select one: a. sum to less than 1 b. be greater than 90° but less than 180° c. each be greater than 45° d. sum to greater than 90° (if they are both less than 90°). e. have cosines less than...

Homework Statement In 3d coordinate space any two of the coordinate angles must A. Sum to less than one B. Be greater than ninety but less than one eighty. C. Each be greater than forty five degrees D. Sum to greater than 90 ( if they are both less than 90) E. Have cosines less than...

Homework Statement If u know the value of two coordinate angles there is an ulimeted amount of possibility for finding the third coordinate angle A. True B. False Homework Equations The Attempt at a Solution I .not too sure about this one any suggestions would be appreciated I...

Homework Statement A particle with a unit charge enters a magnetic field B = i + j with velocity v = 17k . Find the magnitude and direction of the force on the particle. The Attempt at a Solution Had no issues finding the magnitude. However, when finding the direction of the force...

Inside a triangle $ABC$, there is a point P satisfies $\angle PAB=\angle PBC=\angle PCA=\lambda$. If the angles of the triangle are denoted by $\alpha$, $\beta$ and $\gamma$, prove that $\dfrac{1}{\sin^2 \lambda}=\dfrac{1}{\sin^2 \alpha}+\dfrac{1}{\sin^2 \beta}+\dfrac{1}{\sin^2 \gamma}$

Exist an geometric interpretation for the multiplication of 2 angles? Or exist an geometric interpretation for the square/cube of an angle?

http://i60.tinypic.com/nmntpj.jpg How do you differ what angle for example Vab, Vbc, and Vca are? I notice the reference angle is always 0 degrees but how can you tell for the other two? Thanks in advance.

Homework Statement Two projectiles are launched simultaneously from the same point, with different launch speeds and angles. Show that no combination of speeds and angles will permit them to land simultaneously and at the same point. The Attempt at a Solution I have a rough idea...

Homework Statement Show that, for a given initial speed, te horizontal range of a projectile is the same for launch angles 45° +\alpha and 45° - \alpha The Attempt at a Solution x1 = vi cos (45° + \alpha) x2 = vi cos (45° - \alpha) tcomplete trajectory = 2 vi...

Homework Statement Consider two projectiles launched on level ground with the same speed, at angles 45°\pm \alpha. Show that the ratio of their flight times is tan 45°\pm \alpha. The Attempt at a Solution projectile 1 launched at Θ = 45° + \alpha: vyf1 = vyi1 + gt tapex1 =...

Using http://www.mymathforum.com/download/file.php?id=6171 and writing the relationships: \vec{\rho}\;'=R^{-1}(\phi)\vec{\rho} \begin{bmatrix} r'\\ z'\\ \end{bmatrix} = \begin{bmatrix} cos(\phi) & sin(\phi)\\ -sin(\phi) & cos(\phi)\\ \end{bmatrix} \begin{bmatrix} r\\ z\\ \end{bmatrix} and...

Homework Statement A projectile is fired in such a way that its maximum height is a factor of 4 times its horizontal range. Find the launch angle in degrees Homework Equations h_{max}=\frac{V^{2}_{0}sin^{2}\theta}{2g} Range=\frac{V^{2}_{0}sin2\theta}{g} The Attempt at a Solution...

Homework Statement Suppose I have a relation S(\theta, \phi) = U \frac{c}{2} \cos{^{2} \, \theta} and I want to integrate over \phi from 0 to 2 \pi and \theta from 0 to \frac{\pi}{2} . How do I do this double integral? Do I just do it normally (without any transformation), or do I...

Hello, simple question. My textbook (Bostock and Chandler - Pure Mathematics 1) says something that really surprises me. The bolded part is what shocked me, it seems like such a trivial statement and intuitively true. My book was first published in 1978, so perhaps it is out of date. It...

Hi guys, I was hoping someone may be able to clear something up for me. I have been reading a paper on Quantum decoherence and was curious about what particular point (it could easily just be me misunderstanding) It is commonly noted that the superposition of waves represents all of the...

http://postimg.org/image/3mmlbro1p/ Hi, I just want to know if my proof seems ok. So we can begin with : 1 degrees = 1+1/9 grads we multiply by x to generalize x degrees= x+x/9 grads now, we take x degrees and multiply it by 60 minutes to know how many minutes it makes.We also do the same...

Problem: Find the condition so that the line px+qy=r intersects the ellipse $\displaystyle \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ in points whose eccentric angles differ by $\frac{\pi}{4}$. Attempt: Let the points on ellipse be $(a\cos\theta,b\sin\theta)$ and...

Homework Statement microwave of wavelength 3 are incident to a row of parallel metal rods. The separation of the rods is 10cm. The first order diffraction is observed at 25° to the direction of the incident wave. Determine the angle between the first and the second order of diffraction maxima...

Hello, i'm doing some revision and working through the textbook my course follows and have a small problem. The question is an incomplete table of values for sinθ, cosθ, tanθ, \alpha and θ. I have to work out the blanks using what is given. I thought I knew the correct method of doing...

Homework Statement Solving for base angles in a congruent triangle One of the base angles in a congruent triangle is 3x+5 The other base angle is unknown The remaining angle is x+16. Homework Equations See attached PDF The Attempt at a Solution Because two base angles in a...

I'm not sure whether this falls in the homework category, or the standard calculus section, so apologies in advance if this doesn't fall in the right category. Homework Statement Evaluate ∫∫∫e^[(x^2 + y^2 + z^2)^3/2]dV, where the region is the unit ball x^2 + y^2 + z^2 ≤ 1. (or any...

Homework Statement It turns out there is a relation between angle a and angle b. I can't figure it out, could someone give me a hint? There's a lightray that is bouncing from two mirrors (m1 and m2). The angle between those two mirrors is called a. The angle between the incoming lightray l1...

Homework Statement What are the angles between lone pairs in H2O? I know that the bonds are separated by 109.5°. What about the lone pair angles? I googled everything. I found nothing. I cannot directly assume it is 109.5°... I have a basic knowledge of VSEPR.

Homework Statement I know the area of a right angled triangle, I also know the ratio of the two non-hypotenuse sides. Is there anyway of finding the lengths? Thanks! Homework Equations I don't think there are any like Area = 1/2abSinC The Attempt at a Solution I obviously...

Homework Statement Given that a vector has a magnitude of 6.0 units and makes an angle of 45° and 85° with the x and y axes, respectively, find the x and y components of this vector. Does the given information determine the z component? What can you say about the z component? Homework...

Homework Statement Today my teacher asked me "What are the best 2 angles to use when wanting to get maximum horizontal distance while on an elevated surface of 50m." As in Dx. What would these 2 angles have to be for the projectile to go the furthest distance horizontally and what would the...

1) Given: two ropes of negligible weight suspend an object weighing 50N from the ceiling There are two angles of PHI that form from as a measure from the vertical. PHI1 + PHI2= 60°. The tension of the left rope is given to be 80N and the tension of the left rope is given to be 70N. The entire...

Homework Statement a) A light-source at rest in an inertial system S' is emitting light with angle θ' relative to the x'-axis. The System S' is moving at speed v (along the x-axis) relative to the laboratory system S. Show that the emitted light is making an angle θ with the x-axis of...

Hi, I'm trying get a better understanding of Bell's inequality in the form $$\left|E\left(\bf{a},\bf{b}\right) -E\left(\bf{a},\bf{c}\right)\right|\leq 1+E\left(\bf{b},\bf{c}\right)\enspace.$$ I'm considering the Bell state $$\left|\psi\right\rangle=...

Was reading a book on rigging and it had this note that intrigued me: Ensure that the sling angle is always greater than 45° and preferably greater than 60°. When the horizontal distance between the attachment points on the load is less than the length of the shortest sling leg, then the...

Homework Statement A space station observes a high-speed rocket passing by at speed β c in the +x direction. The rocket suddenly emits a light ray from a powerful laser. According to the space station, the light ray was emitted at an angle of θ with respect to the +x-axis. However, the...

1 Gripper C of the industrial robot is accidentally subjected to a 60 lb side load directed perpendicular to BC (see attachment). The lengths of the robot's links are AB = 22 in and BC = 18 in. By using the moment components method, determine the moment of the force about the center of joint A...

Greetings; I am a firefighter so physics is pretty much Greek to me. I work primarily as a rope rescue/USAR tech. We work a lot with rope, pulley's, and anchor points. All of these systems have angles that affect the loading in our system. Now I been taught rules of thumb when constructing a...

Homework Statement Figure below is an overhead view of a 12kg particle that is to be pulled by three ropes. One force (F1, with magnitude 50N) is indicated. Orient the other two forces F2 and F3 so that the magnitude of the resulting acceleration of the particle is least, and find that...

Homework Statement A spaceship of mass ##m_0## moves in the absence of external forces with a constant velocity ##v_0##. To change the motion direction, a jet engine is switched on. It starts ejecting a gas jet with velocity u which is constant relative to the spaceship and directed at right...