Trigonometric Definition and 1000 Threads

Homework Statement http://img362.imageshack.us/img362/1465/problemcn2.jpg http://g.imageshack.us/g.php?h=362&i=problemcn2.jpg Homework Equations http://img510.imageshack.us/img510/3137/formula1df4.jpg http://g.imageshack.us/g.php?h=510&i=formula1df4.jpg...

Homework Statement Verify the possibility of an identity graphically. (Completed this part) Then, prove each identity algebraically. \dfrac{sinx+tanx}{cosx+1}=tanx Homework Equations tan\theta=\dfrac{sin\theta}{cos\theta} cot\theta=\dfrac{cos\theta}{sin\theta}...

Homework Statement 2 cos^2 x + cos x = 0 and tan x = 3^1/2 Homework Equations .. ?? Unit circle. The Attempt at a Solution for the first, well I tried factoring to isolate x, but it really did not work i keep making up my own rules that end up messing with the entire equation...

Homework Statement 1/\sqrt{}2 cos 15 - 1/\sqrt{}2 sin 15 The Attempt at a Solution I got \sqrt{}3/2. If anyone could confirm this, I would appreciate it. Thanks.

I need to solve for x, but,.. honestly, i haven't got a clue for where to begin, or even,.. oy, not sure here are two of my problems: sin x = (3^1/2) / 2 and 2 cos 2 x + cos x = 0 I know I'm supposed to use the unit circle,.. well, maybe any help at all would be very much...

Can someone please give me some tips on how to solve this? : 400*(2,2*cosV-1)*tanV=20*9,81, I am supposed to find V, but I can't see how to solve this equation.

Evaluate sin(tan^{-1}(\frac{1}{3})) 3. The Attempt at a Solution Let y = tan^{-1}(\frac{1}{3}) <=> tan(y)=1/3 y = ? sin(tan^{-1}(\frac{1}{3})) = sin y I think for solution to exist tan^{-1}(\frac{1}{3}) must be in the range of sin, (that is \left\frac{-\pi}{2}...

Homework Statement I'm learning now about darivative all by my self (without a teacher) and I'm not sure about this development Homework Equations The Attempt at a Solution Y=senx y+{\Delta}Y=sen(x+{\Delta}Y) {\Delta}Y=senx*cos{\Delta}x+ sen{\Delta}x*cosx What about...

Homework Statement Find I = \int_0^{2\pi} \frac{1}{cos\phi+b} d\phi Homework Equations Given above.. The Attempt at a Solution This problem is an introductory problem to trigonometric functions and here is how the answer is obtained - but I have a question about it. First, here...

The question is: Use x = \tan \theta , \frac{-\pi}{2} < \theta < \frac{\pi}{2} to show that: \int_{0}^{1} \frac{x^3}{\sqrt{x^2+1}} dx =\int_{0}^{\frac{\pi}{4}} \tan^3 \theta \sec \theta d\theta Using that substitution, I got it down to: \int_{0}^{\frac{\pi}{4}} \frac{\tan^3...

Homework Statement I'm attempting to prove that 1 - sin^2 t /(1 + cos t) - cos^2/(1+tan t) = cos t sin t 2. The attempt at a solution I've tried various approaches. The most promising has the LHS reduced to: (sin t cos t (1 + cos t + sin t cos t))/((1 + cos t)(cos t + sin t))...

Homework Statement lim x --->0 [tan(2+x)^3 - tan8]/x Homework Equations f'(a)=lim h-->0 f(a+h)-f(a)/h The Attempt at a Solution should i differentiate first? am i allowed to do that?

Im supposed to verify that (1-sinx)/(1+sinx) = (secx-tanx)^2 RHS = (secx-tanx)^2 = (1/cosx - sinx/cosx)^2 = [(1-sinx) / cosx]^2 = [(1-sinx)(1-sinx)]/cosx^2 = (1-2sinx+sinx^2)/(1-sinx^2) From here, I'm feeling pretty confused. I'm not even sure if all my values are correct.

Homework Statement Given: sin x + sin y= a cos x + cos y=b find tan(x+y) Prove it to be equal to" \frac{2ab}{b^{2}-a^{2}} The Attempt at a Solution I get stuck after this: 2ab= 2 sin (x+y)+sin 2x+sin 2y b^{2}-a^{2}= cos 2x + cos 2y + 2 cos (x+y) Division of the two never...

How do I find the derivative of cos2x? Do I use the chain rule? u=2x u'=2 y=cosu y'=-sinu dy/dx=-2sin(2x) Edit: Sorry. I mean derivative, not integral.

[SOLVED] Derivatives of Trigonometric Functions I need to find the critical numbers of this function: y = cos x - sin x where -pi <= x <= pi I found the derivative as: dy/dx = -(sin x + cos x) But when I equate dy/dx to zero, I get: sin x + cos x = 0...where do I go from here?

Hi there, I am struggling to solve for x in the following problem:- Find all values of x in the interval 0<= x <= 360 for which: tan^2(x) = 5sec(x) - 2 I have used the identity tan^2(x) + 1 = sec^2(x) to get: sec^2(x) - 1 = 5sec(x) - 2 and rearranged to get sec^2(x) - 5sec(x) +...

cos(4x) + \sqrt{2}cos(3x) + cos(2x) = 0 --------------------------------------------------- Ok, so break down everything to a double angle and i get: 2cos^2(2x) - 1 + sqrt(2)*(sqrt((cos(2x) + cos^2(2x))/2) - sqrt((1-cos^(2x)*(1-cos(2x))/2) + cos(2x) = 0 ...which is quite complicated to...

Homework Statement 1) COS4\theta-COS2\theta/SIN4\theta-SIN2\theta=-TAN3\theta 2)sinx/cosx+1 + cosx-1/sinx = 0 Homework Equations 1) Verify 2)verify The Attempt at a Solution 1) cos(2\theta-2\theta)-cos2\theta / sin(2\theta+sin2\theta)-sin2\theta when simplified i get...

i want the most general solution for sin6x=sin4x-sin2x

Homework Statement Reduce the following series to the most simplified form: 1. 2 sin^{2}(\theta/2)*(1+cos\theta)*(1+cos^{2}\theta)(1+cos^{4}\theta)... 2. tan (\theta/2)*(1+sec \theta)(1+2\theta)(1+sec 4\theta)....... Homework Equations For problem 1: 2...

Homework Statement \int\frac{1+\sqrt{cosx}}{sinx} Hi , I really need a help for this Homework Equations The Attempt at a Solution \int\frac{1+\sqrt{cosx}}{\sqrt{sin}\sqrt{sin}} \int\frac{1}{sinx} + \int\frac{1}{\sqrt{sinx}}\sqrt{}\frac{cosx}{sinx} = \int cscx +...

using those formulas, how would you solve tan 11 pi ----- 8 and cot 195 also, how would you prove tan (x +y ) = tan x and tan ( pi/4 -x) = 1 - tan x --------- 1 + tan x thank you so much for any help

Homework Statement Evaluate the Integral: Sqrt[(X^2)+9] Homework Equations I know its an Integration By parts problem, but I don't know how to start it. The Attempt at a Solution Im JUST learning this as I type this problem out, I've just been stuck on it for a while and my book...

Homework Statement http://imageshack.us" how are the solutions of the fourth roots pi/2? how do you get pi/2, you know the thing after "cos" and "isin" ?

Is this correct? (bcos30-85.7)(bcos30-85.7)=b²cos²30-85.7cos30-85.7bcos30+85.7²

0=-85.7cos(theta)+bcos30-85.7 0=-85.7sin(theta)+bsin30 Can someone please tell me what I am doing wrong. theta=sin^-1(bsin30/85.7) then sub that into the first equation. I then solved the equation on my calculator and it gave me 9999999999 which i know is wrong.

Homework Statement A = [ b c ... 0000000000000000000 ] [ c b c ... .000000000000000 0] [ ... ] [ 000000000000000000 c b c ] [ 000000000000000000 b c ] where a,b are real. This matrix is tridigonal and symmetric. I need to...

Homework Statement Hey, it's me again. This method is giving me some trouble. This is the first problem: \int^3_0\ x^2\sqrt{9-x^2} \ dx The second problem is: \int\frac{dx}{\sqrt{2x^2+2x+5}}. How do I use a trig. substitution to start on this one? Homework Equations The Attempt at a...

Homework Statement Hey folks, I believe I'm right in what I've done so far. I'm looking for confirmation of my methods and also wondering how to finish the first one by subbing in pi/6 for x and keeping pi in the answer. Thank you for your help. Cheers. \int^{\frac{\pi}{6}}_0 sin^2(x)\ cos^3...

[SOLVED] Question involving trigonometric identities and inverse functions Homework Statement http://img141.imageshack.us/img141/2651/quiz1question5zi8.jpg Homework Equations I've tried to combine the following known equations to come up with a solution: \frac{d}{dx}(sin^{-1}x) =...

I am not sure of the way in which I am solving. I am showing my approach and my questions are at end. Plz advise why I maybe wrong? Thanks Asif Problem Statement: Use the formula for sum of a geometric progression to compute exp(i\theta) + exp(i2\theta) +...+exp(in\theta)...

First I wanted to say hello, that I'm new to the forum, and very glad to have found you! I am having a terrific time with verifying my trig identities. I have done ALL odd probs in my text, and am repeating them. The problem that I am having is that I do not see a clear path from one side of...

[SOLVED] Integration with Trigonometric Substitution Homework Statement Given integral (I): I[(x)sqrt(9-x^2)dx] by words: Integral of "X" times square root of "9-X(squared) Use proper trigonometric substitution to solve this problem. Homework Equations The Attempt at a Solution

I have a few quick problems concering evaluating integrals by trigonometric substitution. I guess I will just post five that way if anyone can help with any, would be greatly appreciated. Also: if anyone could inform me on how to input the actual equations onto this forum as I have seen in some...

Homework Statement Integrate cos^n x cos nx Homework Equations Integration by part equations, trigonometric integrals The Attempt at a Solution I was given the hint that this integration involves integration by part and trigonometry integrals. I tried integration by part, by...

Homework Statement The integral of cos[x]*(sin[x])^5dx Homework Equations The Attempt at a Solution I split it into cos[x]*(sin[x])^2 * (sin[x])^2 * sin[x] then each sin^2[x] term becomes (1-cos[x]^2) so you end up with the integral of cos[x]*(1-cos[x]^2)^2*sin[x]dx let...

[SOLVED] Trigonometric Transformation This is a calculus 3 problem, but this part involves only trig identities: Make the function f(x,t) = sin(t)*sin(x) into the form: f(x+t)+g(x-t). I'm not sure whether to use half angle formulas, or what?

Hi, I had a question about the following problem: http://calcchat.tdlc.com/solutionart/calc8e/01/c/se01c01067.gif Can someone explain how sin(0)/0 = 1?

Why do some problems return the wrong answer while others do not on the ti-89. For example: \[ \lim_{x \to 0} \frac{\cos\theta \tan\theta}{\theta}\] Shows up wrong (shows up as pi over 180). But \[ \lim_{x \to 0} \frac{\sin x(1 - \cos x)}{2x^2}\] does not?

Help with a Trigonometric identity... Homework Statement (sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x Homework Equations sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x The Attempt at a Solution solving left side, =[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos...

Homework Statement \int\frac{secx}{(tanx)^2}dx The Attempt at a Solution I tried all the u subs u=tanx and u=secx but neither worked. Should I used other methods? Please help me with the start!

Homework Statement (1-cos^2x)(1+tan^2x) = tan^2xHomework Equations N/AThe Attempt at a Solution (1-cos^2x)(1+tan^2x) = tan^2x L.S. = (sin^2x)(1+sin^2x/cos^2x) = sin^2x+(sin^4x/cos^2x) Now, I get a common denominator, but it's not doing anything for me. Did I do the right thing in converting...

Homework Statement tan^2x = 2tanx*sinx Homework Equations N/A The Attempt at a Solution tan^2x = 2tanx*sinx (tan^2x)/tanx = (2tanx*sinx)/tanx tanx = 2sinx sinx/cosx = 2sinx cosx = 1/2 x = pi/3 \alpha = pi/3 and 5pi/3 Not sure what I'm doing wrong. The...

Homework Statement sinx + cosx = 0Homework Equations N/AThe Attempt at a Solution sinx + cosx = 0 sinx = -cosx sinx = (+/-) sqrt(sin^2x - 1) (sinx)^2 = (+/-) sqrt(sin^2x - 1)^2 sinx = sin^2x - 1 Not really too sure what to do from here on. The answer is 3\pi/4 and 7\pi/4. I appreciate the...

Acos(A*x)-Bcos(B*x)=0, where A>B Is there a general solution for an equation of this form? Thanks, intangible

Homework Statement Determine the points of intersection for the two given functions on the interval 0<x<4pi y = 2 \sin \frac{x}{2} y = 3 \cos \frac{x}{3} 2. The attempt at a solution Well i tried graphing it and found out that the solution must lie somewhere between pi and 2pi...

1.A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle between the string and the horizontal decreasing when 80 m of string has been let out. Answer is 0.02 m/s 2. What I did was: -Drew a triangle as prescribed above -I found the unknown...

Homework Statement Maybe I'm just blind, but how is T_n(x)=\left(\frac{1+\cos(t-a)}{b}\right)^n of the form T_n(x)=\sum_{k=-n}^nc_ke^{ikx} ? I can get \left(\frac{\cos(t-a)}{b}\right)^n by setting c_{\pm n}=\left(\frac{e^{\mp ia}}{2b}\right)^n and the rest of the c_k= 0, but how does...

I need some help on 15 identities problems to help me study for my math final. They are blurry and somewhat hard to read, but if anyone wants to take a crack at some of them they are here: http://img407.imageshack.us/img407/5696/math1lh2.jpg...