Trigonometric Definition and 1000 Threads

Hi, as I was studying complex numbers today I came across this, and I couldn't explain it: 1=e^{i0} 1=e^{i2\Pi} 1^{1/2}=e^{i2\Pi/2} 1=e^{i\Pi} 1=-1 Where is the mistake? Thank you very much for your help.

I remember learning an iterative method that gives the answer to trigonometric polynomials such as sin(x)-0.7-0.611cosx = 0 where x is the angle in degrees. The person who I learned this method from called it the method for solving transcendentals. Now I can't seem to find any...

Homework Statement Find the range of the function: y=(2cosx+1)/(2cosx-1) algebraically Homework Equations Reducing it, I obtained: y= tan(3x/2)/tan(x/2), but the discontinuity confuses me The Attempt at a Solution I did it with my calculator and this is the result: Ran =...

[SOLVED] Series with Trigonometric funtions Homework Statement Determine whether the series converges conditionally,converges absolutely or diverges. \sum_{n=2}^{\infty}\frac{\sin (n+\frac{1}{n})}{\ln (\ln n)} The Attempt at a Solution \frac{\sin (n+\frac{1}{n})}{\ln (\ln...

Homework Statement Determine whether the series converges and diverges. \sum_{n=3}^{\infty}\ln \left(\frac{\cosh \frac{\pi}{n}}{\cos \frac{\pi}{n}}\right) The Attempt at a Solution \sum_{n=3}^{\infty}\ln...

This isn't really a homework question--but just something I was thinking about while doing homework. Since lim(sinx/x) as x--->0 = 1 does that mean that lim(x/sinx) as x--->0 = 1 ?

I'm not sure about answer.It looks very strange. Homework Statement \int_{1}^{e}\frac{dx}{x\sqrt{1+ln^2x}} The Attempt at a Solution for u=lnx-->u'=1/x \int \frac{du}{\sqrt{1+u^2}} substituting u=tan\theta =\int \frac{d\theta}{cos\theta}=ln|sec\theta+tan\theta|...

Homework Statement Find d^2y/dx^2. y = x cos x The Attempt at a Solution I've been doing derivatives recently and now got into doing them with trig functions. I thought it was, y = x cos x = -xsinx = -xcosx but that is the derivative of the derivative. The problem...

Derivative trigonometric functions Homework Statement Find d^{2}x/dt^{2} as a function of x if dx/dt=xsinx Homework Equations The Attempt at a Solution I tried to solve the problem by taking a second derivative of dx/dt=xsinx but I was not sure how to start. Also, it is...

This is an example from the book. Evaluate \int {\frac{{\sqrt {9 - x^2 } }}{{x^2 }}dx} I understand all the steps that get me up to = - \cos \theta \, - \theta \, + C Then the book goes on to explain: "Since this is an indefinate integral, we must return to the original variable...

Homework Statement Three functions are defined as follows: f:x> cos x for the domain 0< (or equal to) x < (or equal to) 180 g:x> sin x for the domain 0< (or equal to) x < (or equal to) 90 h:x>tan x for the domain p< (or equal to) x < (or equal to) q Find the range of f. -1<(or...

\int\sqrt{16-(2x)^{4}}xdx Hint says you may like to use the identity sin(theta)cos(theta)= sin(2theta)/2 However, I think I found a way to use 1-sin^2(theta)=cos^2(theta) First, (2x)^4 = 16x^4 So make it 16(1-x^2)^2. Take the 16 out of the root and the integral and you have...

for x between 0 and 2pie, solve cos(4x)=sin(2x)... is this a proving trigonometric equation? i don't think it is

Homework Statement Un a sequence 0 < x < pi/2 U0 = 2cosx Un+1 = quroot( 2 + Un) 1) Calculate U1, U2, and U3 in function of x (simplify maximum) 2) Show that Un = 2cos( x / 2^n)Homework Equations The Attempt at a Solution 1) U1 = sqroot( 2 + 2cosx) = sqroot( 2 (1 + cosx)) = ?? (now , how...

Question 1 sin theta = 2/3 tan theta < 0 sin2 theta = ?? how would i do this? please help ____ Question 2 solve 2cos^2 theta - cos theta = 1 for 0 <= theta < 2pie how would i do this one too?

Anybody that can show how to deduce cos(a+b) = cos(a)cos(b) - sin(a)sin(b) sin(a+b) = sin(a)cos(b) + sin(b)cos(a) From the relations that we get from eulers formula.. Should be really simple but I think that I have got some relations wrong so I need to se the real solution.:rolleyes: Thanks!

I was doing my exam today and ran into a couple problems. First one: how do you differentiate \tan^2? I converted it into \sec^2 - 1 and used the u/v = (u`v - v`u)/v^2 method, but I would like somebody clever to do it for me, just to be sure, please. Homework Statement Another problem. Rate of...

For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...

more trig... Amm I've been at this problem for an hour already it loooked really easy but for some reason i can't reach the answer (tan x + sec x)^2 = (1 + sin x)/(1 - sin x) soo what went and tried was expand it and then exchage tan and sec.. (sin^2 x /cos^2 x )+ (2/cos x) + (1/ sin^2 x)...

How would one go about solving sin(x) = x/2 I.e. the intersections of f(x)=sin(x) & g(x)=x/2 I can rigorously solve this by going to each individual period and finding the intersections. But is there a better way?

Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?

Homework Statement http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf Question A- (b) They use some trigomentric identity that I don't understand, which one is it? Thanks in advance. Homework...

Homework Statement Prove the following trigonometric reduction using integration by parts: \int \sin^n x dx = - \frac{\ \sin^{n-1} x \cos x}{n} + \frac{\ n-1}{n} \int \sin^{n-2} x dx 2. The attempt at a solution I tried using integration by parts by breaking up sin^n x into sin^(n-2) x...

just encountered this question and kinda confused at how to solve it since I havn't bin told and havn't worked it out for myself. hope you can help. Homework Statement Use the graphs (shows 2 graphs) to find the values of x in the range 0 /leq x /leq 720 when 2sinx = cosx -1 Homework...

Homework Statement Compute \int_{0}^{\infty} \frac{\tan x}{x} {} dx Homework Equations The Attempt at a Solution Got no idea, obviously the derivation differs from the \int_{-\infty}^{\infty} \frac{\sin x}{x} {} dx one. The result I'm supposed to get is \frac{\pi}{2} .

Homework Statement use the inverse functions where necessary to find all solution of the equation in the interval [0,2pi). Use a graphing utility to verify. 2cos(squared)x+3cosx=0 Homework Equations The Attempt at a Solution The answer is pi/2 and 3pi/2 from my teacher.. ===...

Hey I'm just having trouble with this question Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 deg. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors...

How do I get the derivative of y=tan4x The answer in the back of the textbook says (4/cos^2(4X))

Homework Statement I can't seem to find online how to calculate the error propogated by trigonometric functions. That is, I know the uncertainty in \theta but am not sure how to deal with it when I apply the tan function. I am quite okay with how to deal with all the basic...

Homework Statement Integral of \int \sin^{11/3}\alpha\, d\alpha Homework Equations \sin^2\alpha = 1 - cos^2\alpha The Attempt at a Solution \int (\sin^2\alpha)^{4/3}\sin\alpha \, d\alpha \int (1-cos^2\alpha)^{4/3}\sin\alpha \, d\alpha u = \cos\alphad du = \sin\alpha\...

Homework Statement Prove the following identity: (1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta) Homework Equations cos^2 \theta + sin^2 \theta = 1 The Attempt at a Solution I've squared out the first bracket so that it becomes 1 + cos^2 \theta and multiplied out the second bracket so...

Homework Statement Simplify The problem is either 1+[(cosx)/2] or 1+[cos (x/2)] The first one looks unworkable so I'm going with the second...unless any of you see that the first one looks normal... Homework Equations I derived/proved some below... The Attempt at a...

Greetings my friends: I have been reading a book about optimization and I found the following trigonometric equation: tan(10x.pi)= - 10 pi x (this equation goes from x E [-1,2] it is easy to see that has infinite solutions, but the author came to the conclusion that the solutions are...

Hi. I need to prove the following identity \arccos{z} =i \ln { z + (z^2 -1)^\frac{1}{2} } I was given a hint to write \cos{A}=z, then rewrite \cos{A} in terms of the exponential. \cos{A}=\frac{\exp{iA}+\exp{-iA}}{2}=z I took the log on both sides and got stuck at that...

In my book, (cos4x)^2 is written 1+cos8x without referring to any formula. Which trig. identity is used here?

Can anyone help me solve the following problems? sec theta -1/1-cos theta = sec theta tan (pie/2 - theta) tan theta =1 Thanks

I need to solve sin(ax)sin(bx) - k cos(ax)cos(bx) = -1 where k > 1 is constant and so are a and b, and they are all irrational. (It's part of a much larger question in optics...) Any ideas, please? Thanks

Hi, all I am new to this site and I was wonder if anyone could help. I took linear algear algebra last semster and am currently taking statics. I want to know if I can use some of the techniques I learned in linear algebra to solve simtultaneous equations which involve sine or cosines For...

I just came across a problem that wants you to solve for csc of an angle in radians... However, I'm confused about the answer given. Here is the problem: Find the csc when t=-2pi/3, which is equivalent to -120 degrees right? I got -2sqrt.(3)/3 but the answer in the back is -2sqrt.(3)/2...

I was wondering if someone would be able to help me with the following questions: -A progessive wave has amplitude 0.40m and wave length 2.0m. At a given times the displacement y=0 at x=0. Calulate the displacement at (a)t=5sec (b) t=0.8sec -A progessive wave has amplitude 2.5m and a time...

Hi, I'm having trouble understanding how my math book factored the following equation. [(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))] to get [(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))] I get the numerator but I don't understand what happened...

hey I have this question and have looked it up in the textbook and web sites but can't seem to find what to do! Any assistance would be appreciated thanks! Find the first derivative w.r.t the relevant variable 5^(sin(theta)) I am guessin the relevant variable is theta but I don't even no...

Hi. Are there any addition theorems for inverse trigonometric functions? Like arccos(x+y)=? or something... I was wondering about this when I tried to find the derivative of f(x)=arccos(x) by setting f'(x)=\frac{\arccos(x+\Delta x)-\arccos(x)}{\Delta x}

Hi, I have an exam on trig integrals tomorrow and need to freshen up on some basic trig rules (i.e. d/dx of sin(mx) and trig identities such as sin^2(x)+cos^2(x)=1) I was curious if anyone new of some good websites that reviewed all common trig identities used in calculus. Any help is...

Alright, moving on to the topic of taking the derivative of a trigonometric equations, I have been given the problem to find the equation of the tangent line to the curve at the given point for: y = 1/sinx+cosx at (0,1) Now we know that the equation is y-1=m(x-0), so I've tried solving for...

need some assistance with the following integral: \int_0^{2\pi} cosx/(a-cosx), a-parameter (say a>0) i've converted it into a complex contour integral over z=e^(ix): ~ \int_{|z|=1} dz (z^2+1)/[z(z^2-2az+1)] which is easily evaluated for a>1. my question regards a<1 - i am not sure...

Find dy dx 1.) y = In __x2 (x+1)___ (x + 2)3 2.) y = x3 ( 3lnx-1) 3.) y = __cos6 2x__ (1-sin2x)3 4.) y = __tan 2x__ 1- cot 2x 5.) y = x e (exponent pa po ng e) sin2x 6.) Arc tan...

Hi, I have a question about a problem: 1/2csc(THETA)sec(THETA) I have to find the identity for it and I know that csc is 1/sin and sec is 1/cos but after that I don't see where it can lead to a simple answer. If anyone knows it would be helpful, thanks!

Hi. I have to show that x(t)=c1 cos(wt) + c2 sin(wt) '(1)' and x(t) = A sin(wt + phi) are equivalent. I know I have to use sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) or cos(alpha +beta)= cos(alpha)cos(beta) - sin(alpha)sin(beta) I have been strugling with this...

hey just wonderin if any1 could give me a hint as to the best method to prove the following trigonometric indentity: sin^4x-cos^4x = 1 - 2cos^2x i tried the side more complicated first...but can't seem to hav any luck...other then maing it more complicated! umm the x's are meant to be...