Angles Definition and 892 Threads

Homework Statement Let a be a unit vector and b be a non-zero vector not parallel to a. Find the angles of the triangle, whose two sides are represented by the vectors √3(a x b) and b-(a.b)a Homework Equations The Attempt at a Solution The third side will be equal to \sqrt{3}(a \times...

i'm kind of confused with what i read from my book in trig which says "there's a one to one correspondence between the length of all arcs in the Unit Circle and the set of real numbers." my understanding to this is that there's a corresponding real number to the length of all arcs of the unit...

Homework Statement I am trying to figure out how to solve for problems that give a function and ask for the critical points. However, the ones I am having difficulty with are the ones that have multiple trigonometric functions included in them.Homework Equations Find the critical points of the...

Confusing Solid And Plane Angles ! Supplementary Quantities - 1.Solid Angle - Steradian 2.Plane Angle - Radian Doubts - 1.What Is The Use Of Supplementary Quantities ? Physical Quantities Are Used To Measure For Example .. To Measure Length - m Current - ampere Etc... What Can I...

I have done a fair bit of mathematical and 3D modelling of independent automotive suspension systems, and have come to the conclusion that the in pure steady state cornering no matter what the combination of springs, ARB/sway bars, motion ratios or linkage geometry, the roll angle (ignoring the...

I have a sailboat with 2 solar panels installed. They work well, except at the end of the season when the days are shorter, the nights are longer and the sun is lower, so I built a mechanism to tilt and rotate the panels so that they could be pointed directly at the sun. With low sun angles I...

Homework Statement A football player attempts a 30m field goal. If he is able to impart a velocity u of 30 m/s to the ball,compute the minimum angle θ for which the ball will clear the crossbar of the goal. (Hint: Let m = tanθ .) Homework Equations V0x = V cosθ V0y = V sinθ We get t...

Homework Statement "A ball rolls off an incline plane. The speed of the ball is 22m/s and the plane is inclined at 32 degrees to the horizontal.If the incline is 9.0m above the ground, how far from the base of the incline will the ball hit the floor?" (The rounded answer is supposed to be...

Homework Statement An Antenna that is 90 feet high is on top of a hill. From a point at the base of the hill, the angles of elevation to the top and bottom of the antenna are 28.5° and 25°, respectively. To the nearest whole number of feet, how high is the hill? A, 189 ft B, 213 ft C...

Homework Statement A cart of mass 357g is sent traveling down a frictionless sloped track. It's acceleration is 1.65ms-2. 1. Draw a labelled free body diagram of the cart while it is accelerating down the track. 2. Using Newton's second law, calculate the slope of the track. Homework...

I apologize upfront, as I have no experience with math to begin with. However, I have a real life problem I am trying to figure out here at work and I would appreciate some help. Here is my situation: Homework Statement In a 3 dimensional plane, I have an artillery piece pointing at...

Hi all, How would you determine the angle i in the following equilateral triangle. Thank you.

I'm modeling a single 3D rigid body in preparation for some more complicated modeling in order to gain a better understanding of Euler angles, the angular velocity vector and the rotating coordinate system. The body is rotated in inertial frame by an intrinsic ZXZ rotation, with respective...

Homework Statement A fire hose held near the ground shoots water at a speed of 6.8 m/s. At what angle(s) should the nozzle point in order that the water land 2.0 m away? Why are there two different angles? ax=0 xo=0 x=2.0 m ay= 9.80 m/s/s y0=0 y= I'm guessing 0, because it lands on...

Homework Statement In a ##\Delta ABC##, angle A is greater than angle B. If the measures of A and B satisfy the equation ##3\sin x-4\sin^3 x-0.75=0##, then angle C is equal to A)##\pi/3## B)##\pi/2## C)##2\pi/3## D)##5\pi/6## Homework Equations The Attempt at a Solution The...

Homework Statement At a temperature of 18°C a beam of diffracted monochromatic x-rays is observed at an angle of 150.8° to the incident beam after being diffracted by a crystal with cubic structure. At a temperature of 318°C the corresponding beam makes an angle of 141.6° with the incident...

Homework Statement I'm in a Year 10 Physics class, and we have been doing an experiment about Snell's Law (θincident = θrefracted). The experimental design is fairly simple: a beam of light (from a ray box with a single slit in front of it) is shone into a glass block. The angles of the...

Homework Statement Please refer to the image Why is y 109 degrees?(given by my teacher) Homework Equations None. The Attempt at a Solution There are four atoms around the carbon atom, I assumed it to be tetrahedral. Why is that wrong?

A, a'...a''? im in the process of typing out an idea I had about triangles, and I wanted some input, but I ran into a problem when I realized I do not know how to denote multiple "prime" angles. In this diagram, I am working with the corners of a triangle, but have extended the rays outwards...

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1. A basketball will be launched of height h and will hit the hoop that has a height of H. The horizontal distance between the ball and the hoop is d. Given an initial velocity Vo write both possible launch angles in function of h, H, Vo and d 2. theta=tg^-1(Vy/Vx) (1)...

Question Find all the values of ∏ in the interval 0 < θ < 2∏ for which 2cos2 θ – sin θ = 1, giving each answer in terms of ∏ I think the question is asking me to find the values of θ in terms of ∏ for all values between 0 < θ < 2∏ This is what I have done so far I have worked...

Homework Statement http://grab.by/lp4S This probably shouldn't be too hard, but I'm getting pretty stuck. On the attached picture, the angles 67.4 and 22.6 are given, but I am not sure how they were found. Taking all the given information on the picture (besides those two angles), how...

Are 6 degrees, 5 degrees, and 7.5 degrees constructable? So based on the theorems that I know, these angles are constructable iff the cos\vartheta is constructible. So all that is left for me to do is show if cos\vartheta is constructable. For 6 degrees, I tried to get a relatonship with...

We know that in triangle ABC angle A equals $$\alpha$$ and side $$a=\frac{b+c}{2}.$$ How to find angles B and C knowing that $$B\geqslant C$$? For which values of $$\alpha$$ the problem has solutions? ps. a, b, c are only notations. answer. $$\frac{\pi-\alpha}{2}\pm\arccos(2\sin\frac{\alpha}{2})$$

Homework Statement This is one of my homework questions. I think I have the right answer, but I don't understand how to figure out the "given" angle, so if someone could explain it to me, that would be great! Be sure to look at the picture attached...it's what's tricking me. A prism...

Let $$ABC$$ be a triangle such that $$\frac{BC}{AB-BC}=\frac{AB+BC}{AC}$$. Determine the ratio $$\frac{\angle A}{\angle C}$$.

1.So the problem is actually two parts. There's a block on an inclined 30degree plane and 3 different forces are acting on it.F1 is parallel to the plane is looks as though is the resultant force going up the plane in front of the block. F2 is acting at an angle 30degrees from the incline. So if...

Homework Statement Sin(tan(2x)) With respect to x Homework Equations Differentiation The Attempt at a Solution My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ? Or do I have to convert to sine/cosine and go from...

Homework Statement Estimate to the nearest degree, the angles that a diagonal of a box with dimensions 10cm x 15cm x 25cm makes with the edges of the box.Homework Equations cos\theta =\frac{u\cdot v}{\left \| u \right \|\left \| v \right \|}The Attempt at a Solution For the angle between the...

Homework Statement I'm having a problem with this. I was told to use the difference of sums formula. I'm not exactly sure of what that is/means.Homework Equations Difference of sums?The Attempt at a Solution I'm thinking that Cos(a)=1/3 refers to 1 being the adjacent angle and 3 is the...

Find the missing angles in each of the following:

Homework Statement Fb is the spring balance which measures the total tension in the string. So T1 + T2 = Fb The system is at rest so a = 0. Weight W is hanging as shown in the diagram. T1 corresponds with angle α and T2 corresponds with angle β. ONLY THE HORIZONTAL FORCE CONTRIBUTES TO...

Homework Statement In the Compton scattering event seen in the figure, the scattered photon has an energy of 120 keV and the recoiling electron has an energy of 40 keV. Find: a) The wavelength of the incident photon b) The angle θ at which the photon is scattered c) The recoil angle...

Homework Statement I just have to prove the well known identities: \cos(\alpha + \beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta) \sin(\alpha + \beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin( \beta) But the thing is that I've to use the Taylor power series for the sine and cosine...

Hi, first time poster, sorry if this is in the wrong area or has already been asked. I'm looking at a situation like this: except that instead of being lifted via hydraulics, a crane will be attached to one end. The other end will be attached to a concrete slab via a flange, so that it does not...

We're going over the reactivity of aromatic compounds so I was reviewing material over Sn1 and Sn2 reactions. In the book that we have, it says that the smaller the bong length between two carbons, or other atom, in a cyclic compound, the smaller the bond angle. That's where I get confused...

i would like to know if the 'angle' between let's say the walls of a room (ie. the intersection of 3 planes all perpendicular to each other) can be represented in mathematical terms, but as a kind of 3D angle- that is to say not as a combination of 2D angles but as an altogether new form of...

Hello, I have read about Euler's angles and matrices, including zxz,zyz, etc . I am not obliged to use a specific rotation but rather I want to figure out what angles I need to use for alpha,theta, gamma in the specific matrix. For example, I have a vector from the centre with vertex x,y,z of...

Is it possible that a triangle with angles totaling over 180 degrees could exist without being embedded in a 3rd dimension?

Homework Statement I have a problem as follows: "Two charges of identical mass hang from the same point by a thread of length l. One has charge q and the other has charge 2q. Find the angle each mass makes with the vertical." Now, I got an answer and found that each mass will make the...

At time 2:20, the woman says, "Using trigonometry, we know that this angle is the same as this angle." Which trigonometry or geometry property is she referring to that is needed in order to determine those two angles are equal? Is there a name for it? I don't have a geometry book, but I am...

Homework Statement If a Mass let's say a Ball Bearing A with a velocity of 2ms-1 and a mass of 2Kg hits two other ball bearing B & C which is not moving with ball bearing B & C each has a mass of 1kg each. What will happen to ball bearing B & C? Please see attached picture i have the question...

Can someone please explain what neutrino mixing angles are and how they relate to neutrino mass.

Homework Statement Cosx=0. Solve for all angles where 0<x<2∏, and give the general solutions. Homework Equations The Attempt at a Solution Angles: x=∏/2, 3∏/2. General solutions (what I think they are): x=∏/2+n2∏ and x=3∏/x+n2∏ where n is an integer. General solutions (what the textbook...

Hey, I'm guessing this might be as good a place as any on this forum to ask for some ideas. So every week me and friends play a soccer game at a local field. It's basically an empty field and we create our own field of play within it with cones. We have 4 cones, one for each corner of the...

There's a para in my textbook which doesn't make much sense to me: An observer or a fish under water looks up to see a compressed view of the outside world. The 180 degree view from horizon to horizon is seen through an angle of 96 degrees (twice the critical angle). A lens, called fish eye...

Hi, I have been stuck on this question for a while, and I need help figuring it out. For a lab, we had two ring stands set up about 1m apart from each other, with the rings at different heights, and we tied a string between them. We then placed a 200g mass on the string. We had a LabPro with a...

I am a physics teacher and am wondering something about the range equation. Wouldn't that equation work for complementary angles each time? The author of our book has us solving for one angle but shouldn't you solve for two?

I am trying to prove that the two θ are equal from this picture http://en.wikipedia.org/wiki/File:Double_slit.svg How do I go about proving this?