Cos Definition and 318 Threads

I'm currently reading Apostol's Calculus. I'm now on the part where I need to prove sin and cos values for specific values. Right now I'm working on sin and cos of pi/6. However, I always get at 1/2 and √3/2 for the final value. Here's my solution so far: Homework Statement Use the properties...

Homework Statement Recall that a function G(x) has the limit L as x tends to 1, written lim as x -> infinity G(x) = L, if for any epsilon > 0, there exists M > 0 so that if x > M , then |G(x) L| < epsilon. This means that the limit of G(x) as x tends to 1 does not exist if for any L and...

cos theta=pi/2...hint pi/2 is not an angle. Homework Statement \cos\theta=\frac{\pi}{2} HINT:The real number \frac{\pi}{2} is not an angle. Homework Equations The Attempt at a Solution I tried 0=\cos^{-1} \frac{\pi}{2}, but that equals no solution. And if \frac{\pi}{2} were an...

Homework Statement I have to determine whether the series converges or diverges. \sum (cos^2 (n)) / n^2 +1 Homework Equations Suppose An and Bn are series with positive terms. If the limit of An over Bn as n approaches infinity equals C, and C is a finite number greater than 0...

Homework Statement I have no idea how to start. Any hints? Thanks in advance.

Homework Statement integral (sin^4(x) + cos^4(x))^.5 dx Homework Equations sin^2(x) = (1 - cos^2(x)) The Attempt at a Solution cos^4(x) + {1 - cos^2(x)}^2 = 2cos^4(x) -2cos^2(x) + 1 subst u = cos^2(x) integral (2u^2 - 2u +1)^.5

Homework Statement For tan(theta) = /2/3 (theta in quadrant 2) find sin(pheta) and cos(pheta) using the pythagorean identities. Homework Equations The Attempt at a Solution Which 2 pythagorean identities would I use? My trouble is with finding sin and cos from tan.

Hey folks just wondering whether anyone here knew of a series for cos(x) that converges fairly quickly for values between 0 and 2*pi? The 'usual' series takes up to around the 10th term before it starts looking decent for cos(2*pi) for example.

Homework Statement Ok, this is not really a problem, but I need help on understanding the basics of sin, cos, tan, and their inverses. i was looking at http://www.analyzemath.com/DomainRange/domain_range_functions.html and it was saying that the domain for sin and cos is (-inf , + inf)...

Doing a past paper where long story short I have a set of equations and I have to prove the variables are equal to some trig function. Namely: a^2 + c^2 = b^2 + d^2 = 1 ad - bc = ab + cd = 0 Now I know that sin^2 + cos^2 = 1 and that sin(A+B)=sinAcosB + cosAsinB, etc and the...

How would I find cos for tan when.. Tan b = (-√3) Theta lies in quadrant iii Sin b would equal (-√3) / 2 So Cos b would equal -1 / 2?

Homework Statement lim as x-> 0 (xcsc2x)/(cos5x) Homework Equations lim as x-> 0 (sinx)/x = 1 The Attempt at a Solution (x(1/sin2x)) / (cos5x) Not sure what I am supposed to do here! Thanks :)

Homework Statement Find the parametric equation of y = cos x with max at (3, 5)Homework Equations The Attempt at a Solution There aren't any examples of going from y's and x's and turning them into functions of time. They only go from time functions to y and x functions. So I'm pretty lost on...

Homework Statement This would be easier if I knew how to use LaTeX, but I'll give it a shot. Show by explicit integration that the following is true: Integral from 0 to a of sin(m*pi*x/a)*cos(n*pi*x/a)=0Homework Equations The Attempt at a Solution I've used an identity to change...

Homework Statement Sec 50\circ x Cos50\circ Homework Equations The Attempt at a Solution 1 / Cos 50 \circ x Cos50\circ Would they equal to 1?

Homework Statement Sin^{2} 20\circ + 1/sec^{2} 20\circ = 1 ? Because isn't 1/sec the same as cosin? Homework Equations The Attempt at a Solution

Homework Statement I'm asked to derive equation(2) from equation(1). equation(1): d=(tsin(2i))/((n^2-sin(i)^2)^1/2) equation(2): n=sin(i)(((2tcos(i/d))^2+1)^1/2) Homework Equations The Attempt at a Solution My attempts have got me nowhere, and I don't know how to even...

Homework Statement This problem deals with the displacement of a light ray as it travels through a glass medium. Starting with the equation #1: d=S[sin(i)cos(r)-cos(i)sin(r)] (where d=the length of displacement of the light ray in the glass medium, i=angle of incidence...

Homework Statement This is a more general question... but here is a specific example in which I don't know why sin is used where it is and why cos is used where it is. I don't need the problem worked out or anything (I have it worked out by my professor), I just need to understand why sin and...

I have a rather difficult math problem. In my circuits class the professor prefers to express the cosine function using Euler's formula as (ejwt+ejwt)/2. Last semester for the final, one of the problem's solutions (that he gave us) used partial fraction decomposition to solve the Laplace...

Homework Statement Prove:( (1 - cos A)/ (1+cos A) ) ^(1/2) = cosec A - cot A Then they have... ((1 - cos A)/ (1+cos A) ) ^(1/2) = ( (1 - cos A)^2 )/ (1-cos^2 A) ) ^(1/2) = (1 - cos A) / (1-cos^2 A) ^(1/2)/ I have never done anything like this... I have just been studying trig...

So I have a Hermite curve with the control points: //point# (x,y): p0 (1,0) p1 (1,(Math.sqrt(2)-1)) p2 (Math.sqrt(0.5), Math.sqrt(0.5)) I also have the algorithm to find the points on the locus between 0 and 45 degrees: //L0 is the point on the line between p0 and p1 //L1 is the...

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...

i am quite confusing about those reaction force... let say a body is placed on inclined plane with angle @... at equilibrium, what are the forces that balances each other ?? mg cos@ balanced by R or R cos@ balance mg ?? thanks~

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...

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers! Let f(x)=−3x+6 if x<-3 = 15 if x > -3 Find the average rate of change of f(x) on the interval −5<x<5 . The average rate of...

Homework Statement I have this equation, but I'm having trouble solving for the unknown :/ I know that d is 109; I just don't know how to get it. see below Homework Equations -dsin35 = -4.9(dcos35/25)^2 The Attempt at a Solution -dsin35 = -4.9d^2 cos^2(35)/25^2 -dsin35 = -4.9d^2 cos(35) x...

I'd like to apologize for not using the symbols but I spent over 1 1/2 hours trying and after using one of the symbols it wouldn't format correctly for any others. The s^2. s^3 etc... are seconds Homework Statement A particle is moving in one-dimension, and its acceleration in m/s^{2}as...

Homework Statement plot x(t) = 10cos((pi*t)-(pi/4)) Homework Equations pi/4 is the shift to the right 10 is the amplitude of the graph pi is the radian frequency The Attempt at a Solution so i got the amplitude and shift to the right by pi/4 part but as for the radian...

Finding the Equation of Tangent line on cos wave! Find the equation of the normal line to y = 2cos ( 4x) at x = \pi / 3 I don't even know where to start with this question, i have searched the textbook and internet, help would be appreciated.

Greetings all :blushing: Homework Statement Greetings all this is the basic type of problem that I am having. W = F d cos θ. This is not for homework this is for my preparation for an exam. Homework Equations it has to do with the Work:: W = F d cos θ The Attempt at a...

Why does cos θ, which normally equals x, become 0 when you evaluate this function for π/r radians? (π/r means pi over r radians) Why does cos θ, which normally equals x, become 0 when you evaluate this function for π/r radians? It says that the point on the circle for this question is (0,1)...

hi all, its been a while since I've used a scientific calculator, anyway i am having trouble with cos. I've been askes to find the magnitude of the current flowing in the neutral conducter. V = 400 Lv=231 R1= 23 R2=11.5 R3=9.2 I1=10.04 I2=20 I3=25.1 my real trouble is using a...

Hi, if cosine and sine waves are exactly the same wave except cosine starts earlier in time, why do they have different Fourier Transforms? I know the cos would have an impulse at f=Fc with amplitude of 1, and sin would have an impulse at f=Fc and amplitude of 1/j. I don't understand why the...

Maclaurin Series cos x (MATLAB)... can somebody please find my error a. Consider the MacLauren series for cos x. Find TN(x) for N = 2, 4, 6, 8. For each of these, graph cos(x) and TN(x) on the same plot for x (-pi/4,pi/4) y=cos(x); T2=zeros(1,length(x)); for i=1:length(x)...

I am trying to compute the amount of energy received by the Earth from the sun, by integrating over the Earth's surface. I keep reading that the formula should be: E = e-max * cos @ * area e-max is the solar insolation, @ is the angle between the sun and the perpendicular to the land...

Homework Statement This is an example provided by my lecturer in his notes. He puts practically zero working in. When i work the problem through i do not get the same answer as he does. In this section i have copied the exact text from the problem: Find the Fourier transform of...

Hi, I have been trying to solve some mechanics problems and I can come up with the right equation, but I don't know how to solve it... For example: 490.5cos(theta) - 3600cos(theta)sin(theta) + 1800sin(theta) = 0 i need to solve for theta here its one equation and one unknown...

Hi, For this integration by substitution problem, I am not sure whether I should: 1. simplify the problem first, then select U, find the derivative of U, then integrate or 2. use the product rule first (on the upper part of the equation), then select U, then find the derivative of U...

Homework Statement r = r(t) \theta = \theta(t) x = r cos(\theta) dx/dt =dr/dt cos(\theta) - r sin(\theta) d\theta/dtThe Attempt at a Solution Where does the d\theta/dt come from at the end of the derivative? I know I'm using product rule here because r and theta are both functions of t...

Homework Statement Write a user-defined function that determines cos(x) using Taylor Series expansion Stop adding terms when estimated error, E<=.000001 Homework Equations sum Sn = Sn-1 + an E = | (Sn - Sn-1)/Sn-1 | The Attempt at a Solution function y = cosTaylor(x) Sn=1...

Hi! I have learned how to solve equations like: \int^{2\pi}_{0}\frac{1}{1+sin\theta}d\theta using \int^{2\pi}_{0}F(sin\theta,cos\theta) d\theta \int_{C}F(\frac{z-z^{-1}}{2i},\frac{z+z^{-1}}{2}) \frac{dz}{iz} How do I solve equations of the type...

Hello The electric dipole potential is V (\textbf{r}) = \frac{1}{4\pi\epsilon_o} \frac{\textbf{p}\bullet \hat{r} }{r^2} I am trying to figure out the algebra in my book. How do you evaluate the scalar product of the dipole moment and the unit vector in the above equation? I get qd...

Homework Statement I'm wondering how you would find values of sin, cos, tan, sec, csc, and cot without a calculator. I don't have a specific problem but how would you solve things like tan 45 degrees, sec 30 degrees, and cos -30 degrees? 2. Relevant info I have the values of sin and...

Homework Statement Find Cos B Hint: use trigonometry + Geometry http://img210.imageshack.us/img210/4596/pow.png Homework Equations trigonometry + Geometry The Attempt at a Solution I don't see how i could use trig to find any of the angles, and since none of the lins go through the...

Homework Statement Solve the equations: 100sin(\alpha) -400cos(30^{o}-\alpha) = 210 Homework Equations cos(A-B)=cos A cos B + sin A sin B The Attempt at a Solution I threw the identity into the original equation, simplified a bit now I'm stuck at the following: 200sin(\alpha)...

Obtain the forumal of cos( theta 1 + theta2)... This should be a very basic question. I'm reviewing some linear algebra for my Field theory course but there is a question that I'm suck on. It says (a) Prove that P = cos\theta i sin\theta j and Q = cos\phi i sin\phi j are unit vectors in the...

No problem specifically, just more of a method question. I am extremely confused on when to use sin cos and tan. Say for instance it gives me an angle, say theta, and one side. How would I be able to tell what to use sin cos or tan. I know the trick SohCahToa but I really am confused. I am in a...

I think what I'm doing is overkill because all I want to know is when to use sin and cos in the components regarding (isolated) two-dimensional collisions. I'm just showing more content because it might help for context. Also, there are more steps in order to find the final velocity which is...

Homework Statement convert a*sin(bx+c)+d to (mx+d)+a*cosb(x-c) Homework Equations The Attempt at a Solution