Trig Definition and 1000 Threads

How do you know when to use exponentials and trig functions when solving for the wave function in a finite square well? I know you can do both, but is there some way to tell before hand which method will make the problem easier? Does it have something to do with parity?

Please take a look below example (the attached image below). How do I know that the angle ##\sin (\frac{7π}{4})## is corresponds to the coordinates ##(\frac{\sqrt {2}}{2}, -\frac{\sqrt{2}}{2})##? I know that ##\frac{7π}{4}## is 315°.

Trig help please! CNC Machining/Engineering

$$(\cot \theta)(\sin \theta)$$ So far I understand that you can make $$(\cot a) \implies (\frac{\cos \theta}{\sin \theta})$$ Then it would come to $$(\frac{\cos \theta}{\sin \theta})(\sin \theta)$$ I'm stuck at when making $$(\sin \theta)$$ into a fraction. The sine in between the asterisks...

If $$\cos(\pi/3)= \frac{1}{2}$$, find $$\sec(\pi-\pi/3)$$ Someone really give me step-by-step explanation. I really don't know what identity to use, and no idea how to get cosine to secant. Please, it would help. I do have more questions if you help me dissect this problem. XD Thanks so much in...

Can somebody please explain to me why the integral of, for instance, cos((2*pi*x)/a)*cos((4*pi*x)/a) vanishes over the interval 0 to a? As I understand it, this is generally the case when integrating sines and cosines with different arguments "over the interval of a period." But I'm confused...

Homework Statement 7.5Sin(\frac{π}{10}x) = 5Solving for x The Attempt at a Solution [/B] 7.5Sin(\frac{π}{10}x) = 5 Sin^{-1}(\frac{5}{(7.5}) = \frac{π}{10}x \frac{10}{π}Sin^{-1}(\frac{5}{7.5}) = x = 2.32 If this function were a parabola, there would be two answers based on quadratic...

Homework Statement Find f'(x) if f(x) = 8^(sin^2(3x)) Hint: you will need to use the double angle formula for trig functions and your answer should only have one trig function in it. Homework Equations if y=a^u then y' = ln a * a^u * du sin(2x) = 2sinxcosx The Attempt at a Solution We're...

Homework Statement I feel like I this problem shouldn't be that hard, but I can't figure out how to evaluate this equation cosx - cosx*sinx = 1/3 Homework Equations I don't know what to use for this, none of the trig identities seem to help The Attempt at a Solution I tried substituting ##...

Homework Statement A model for the suspension of a vehicle is shown where the spring has stiffness k = 178 N.mm and an unstretched length of 347 mm. Here is the picture: http://i.imgur.com/1dTVs12.jpg Part a asked to determine the value of P and the force supported by member AB so that the...

Hi! I've tried a couple of approaches with this: converting to complex exponential form and using standard trigonometric identities but have been unable to solve. I suspect DeMoivre's formula applies but I don't see how.Prove...

So here is the problem: Find the anti-derivative of sec 3x(sec(3x) + tan(3x)) Now I have tried foiling it out, and I am stuck at the part where I need to anti-derive Sec(3x)Tan(3x). Any help/tips would be greatly appreciated.

I was going to ask a question about whether or not pi was constant or changed with curved space. I found the answer on here that it does indeed change. Then I started thinking about the ramifications of that. sine waves are dependent on pi, so they should change too. Does sin(theta) =...

Homework Statement Okay so the problem is asking simply for a proof for convergence /divergence of the following indefinite integral: ∫(x*sin2(x))/(x3-1) over [2,∞) Homework Equations I know I can use substitution method The Attempt at a Solution Okay so I know if i factorize the bottom...

Hi, I'm currently taking ap calc bc as a senior in high school. Since trig sub and power reduction formula is not apart of the ap curriculum our class is skipping it. Assuming I pass the test and get credit for it, I will probably skip calc 2 in college. If I continue to study math and physics...

A one acre parcel has 2 sides 180 ft and 240 ft intersecting at a right angle. the other side adjacent to the 180 ft is 200 ft what is the length of the 4th side. by Pythagorean theorem $BD = 300$ so triangle ABD = $21600 \ ft^2$ thus triangle DBC = $21960 \ ft^2$ so 21960 = (1/2)(300)(h)...

My trig. is so-so (I honestly hated it) and just curious how much it's used and needed in other maths? Thanks.

$$\cos\left({4x}\right) =8\sin^4\left({x}\right) -8\sin^2\left({x}\right) +1$$ I thought this would break down nice from the quadratic but it didn't.

Homework Statement A spectator is standing 50 ft from the freight elevator shaft of a building which is under construction. The elevator is ascending at a constant rate of 20 ft/sec. How fast is the angle of elevation of the spectator's line of sight to the elevator increasing when the elevator...

1. Given, x + yi = tan^-1 ((exp(a + bi)). Prove that tan(2x) = -cos(b) / sinh(a)Homework Equations I have derived. tan(x + yi) = i*tan(x)*tanh(y) / 1 - i*tan(x)*tanh(y) tan(2x) = 2tanx / 1 - tan^2 (x) Exp(a+bi) = exp(a) *(cos(b) + i*sin(b))[/B]3. My attempt: By...

I have a problem with the integration of $\int \sqrt{x^2 +4x +5} \,dx$ I first started by completing the square ${x}^{2} +4x + 5 = {x}^{2} +4x +4 - 4 +5 $ After I completed the square the integral became $\int\sqrt{{x}^{2} +4x +4 - 4 +5}\, dx = \int\sqrt{{x+2}^{2}+1} \,dx$ Then I did a trig...

Good morning everyone, I have written a free math textbook, and I'd appreciate some feedback on it. It's about the basics of Trigonometry, including sine, cosine, tangent, radians, the unit circle, a bit on identities, and the Law of Sines, Cosines, and Tangents. I wrote it in a rigorous...

Homework Statement I'm having trouble understanding why we solve vector components (i and j, or the horizontal and vertical legs) like a right triangle? An example would be a 5-4-3 triangle. If 5 N was the force vector I am solving for then I would end up with 4 N in the horizontal direction...

Homework Statement $AB = 20 cm$, $m∠A = 30°$ , and $m∠C = 45°$ . Express the number of centimeters in the length of $BC$ in simplest radical form. Homework Equations $sin A = sin C$ The Attempt at a Solution $AB = 20, BC = x$ D is the point where this obtuse triangle separates into 2 right...

What can be said about the arguments of the exponential functions and trig functions ? Can the argument be a vector or must it be a scalar ? If it can only be a scalar must it be dimensionless ?

Consider the function f(x) = ln (cos^2(x)) When is it increasing/decreasing?

Im to solve ##(k+l)^{2}e^{-ila}-(k-l)^{2}e^{ila}=0##, for ## k##, The solution is ##k=l(e^{ial}-1)/(e^{ial}+1)=il tan(al/2)## FIRST QUESTION So it's a quadratic in k, should be simple enough, my working so far using the quad. formula is ##k= (4l^{2}(e^{-ila}+e^{ila})\pm...

There are 2 trig functions on the same set of axis. f(x)=600sin(2π3(x−0.25))+1000 and f(x)=600sin(2π7(x))+500 How do I go about finding the points of intersections of the two graphs? This was from a test I had recently and didn't do too well on,so any help would be much appreciated. I started...

Can you help me how to solve this system of trig eqns $W\cos(30^{\circ})-275\cos(\theta)=0$ $W\sin(30^{\circ})+275\sin(\theta)=300$ I have tried to divide the first eqn by 2nd and I get $\tan(30^{\circ})=\frac{275}{300\cos(\theta)}-\tan(\theta)$ I'm stuck here! Kindly help me please!

As part of a personal musicology project I found myself with the mathematical model of a geometry which utilizes the equation a*(a/b)sin(pi*x) The only problem with this is that I need to take the integral from -1/2 <= x <= 1/2, and according to Wolfram Alpha no such integral exists. I can...

Homework Statement [/B] Hi, I am currently working through a textbook, and the following simplification is given for an example question: I can't seem to work out how they have moved from cos(pi+n*pi) to cos(pi)cos(n*pi) so easily? Is there a simple trick I have missed? I understand the...

Homework Statement I have had a brain malfunction and I need help to understand something simple. It would be great if someone could show the process of attaining the end form. How does; ##a\cos{(x)}+b\sin{(x)} = c\sin{(x+\phi)}## where a,b are arbitrary constants, c results from whatever...

I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these...

Homework Statement The equation of a transverse wave traveling in a string is given by y(x,t) = 10 cos (π/2)(0.0050x - 8.0t + 0.57), in which x and y are expressed in centimeters and t in seconds. Write down the equation of a wave which, when added to the given one, would produce standing...

I need help finding the unknowns $H\cos(\theta)+559.68=750$ $H\sin(\theta)-124.26=0$

EDIT: I figured out my mistake...no option to delete silly post. Oh well. 1. Homework Statement The problem is: use iterated integrals in polar form to find the area of one leaf of the rose-shaped curve r = cos(3*theta). My setup agrees exactly with the solutions manual...but then something...

$\int\frac{1}{\sqrt{2+3y^2}}dy$ $u=\sqrt{3/2}\tan\left({\theta}\right)$ I continued but it went south..

Hey PF, as my thread a week or two ago said I am currently planning on taking a college Calc and Analytic Geometry class with formal education only up to Geometry. I am very proficient in Geometry, good in algebra 1, have some experience in Trig and a little in Algebra 2. For this reason I was...

Hey guys, The problem is #49 and it is a simple calculus problem, but the part that I am confused on is how the solution solves the trig. equation. In the solving, the solution brings out the plus-minus symbol and puts it outside the arccos, but I feel as if it should be inside the arccos. I...

Homework Statement Sin2x-cosx=1 Solve for all x values between [0,2pi) Homework Equations Sin2x=2sinxcosx The Attempt at a Solution [/B] 2sinxcosx-cosx=1 cosx(2sinx-1)=1 I don't know what to do after this. It doesn't equal 0 so I can't set each factor equal to 0

I know that asinx + bcosx can be put into a single trig fom, but can also the above sum be put into a single trig function?

Anyone know a way to calculate x=tan(x)cosh2(x) ? I think I should know - but just blank at the moment.

I'm completely lost here. I've got the cheat sheet of trig rules, but they don't appear to be helping me, I've watched a half dozen videos on each of cos sin and tan, and nearly all of them discuss the wrong topic. I don't want help on any single problem, but advice. How can I make sense of the...

Homework Statement Show that (sin^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1) == -1 Homework Equations Sin^2 x + cos^2 x == 1 The Attempt at a Solution (sin ^4 x + (sin^2 x * cos^2 x)) / (cos^2 x - 1) = ((sin^2 x)(sin^2 x) + (sin^2 x * cos^2 x)) / (cos^2 x - 1) =((sin^2 x)(1 - cos^2 x) +...

Homework Statement 1.\int{\frac{sinx}{1+cos^{2}x}} \, dx 2.\int{\frac{1}{13-4x+x^2}} \, dx Homework Equations Inverse trig identities. The Attempt at a Solution For the first one, I'm not too sure about what to do with the sinx on the numerator and i have tried u-substitution to no avail...

I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can...

Homework Statement [23/4, 2] 4/(x√(x4-4)) Homework Equations ∫ du/(u√(u2 - a2)) = 1/a(sec-1(u/a) + c The Attempt at a Solution I first multiplied the whole thing by x/x. This made the problem: 4x/(x2√(x4 - 4)) Then I did a u substitution making u = x2. Therefore, du = 2xdx. I multiplied by...

Homework Statement ABC is a triangle in which none of the angles is obtuse. The perpendicular AD from A to BC is produced to meet the circumcircle of the triangle at E. If D is equidistant from A and E prove that the triangle must be right-angled. If, alternatively, the incentre of the...

http://i.4cdn.org/sci/1422268953865.jpg

thanks