Trigonometric Definition and 1000 Threads

Homework Statement \int_{1}^{5}\sqrt{4-(x-3)^2}dx Homework Equations The Attempt at a Solution Not really a homework. Just curious. Let x-3=2sin u x=2sin u+3 Now limit change, when x=1, u = arcsin (-1) when x=5, u = arcsin (1) Since there are infinitely many solution...

Hi everyone, In my research project, i am struck with an integration. Can someone help me out: [SIZE="5"]∫ [SIZE="3"]dx/[SIZE="4"]√[SIZE="3"](1-k*sin2x) Thanks, Sandeep

Hello all, I was wondering if someone has ever found a purely algebraic proof for the addition/subtraction theorems of trigonometry, mainly sin(a+b)=sin(a)cos(b)+sin(b)cos(a). Given a right triangle: Let x be one of the perpendicular legs and let the other leg be composed of two parts, y1...

Hi! I'm just a beginner i don't know much about trigonometry... can you tell me how to convert the trigonometric ratios to degree.. for example: o.3333 how did it become 19.47degree ? i saw it in the book... can you tell me how? I know this is simple for you all! i want to solve it without using...

Homework Statement Here is the question given: A blade for a lawnmower consists of two parts made of the same material and joined together as shown: The length OP is one unit in length and MPQN is square in shape. Develop an equation for the cross-sectional area of the blade and...

can somebody help me out on this one,i got stuck on this one https://www.physicsforums.com/attachments/164

Homework Statement Prove that: tan^2∅/tan∅ - 1 + cot^2∅/cot∅ - 1 = 1 + sec∅cosec∅ Homework Equations The Attempt at a Solution I have solved the question taking tan∅ = sin∅/cos∅. But I want to solve it some other way.

Homework Statement lim of (sin(x)/(x+sin(x)) as x approaches 0 Homework Equations none The Attempt at a Solution I tried using trigonometric identites to figure it out but I can't do it, and when I looked up help for it I only found solutions that utilize the l'hopitals rule. I...

Homework Statement Hello! I'm having some trouble to find this limit \lim_{x\rightarrow \pi}\frac{senx}{x-\pi } Also, limits like this one \lim_{x\rightarrow \frac{\pi}2{}}\frac{1-senx}{2x-\pi } confuse me a lot!Homework Equations The Attempt at a Solution I don't even know where to start! I...

it's bothering my brain..i thought about it many times...i can't make intuition of it can anyone prove it? oh by the way... C = Sqrt[A^2 + B^2] and theta is equal to arctan(B/A)

hey, (1-{{x}^{2}}){{y}^{''}}-2x{{y}^{'}}+n(n+1)y=0,\,\,\,\,\,-1\le x\le 1 to convert the legendre equation y(x) into trig form y(cos\theta) is it simply, set x=cos\theta then (1-{{\cos }^{2}}\theta ){{y}^{''}}-2{{y}^{'}}\cos \theta +n(n+1)y=0 for -\pi \le x\le \pi {{\sin }^{2}}\theta...

Homework Statement I'm trying to solve two similar equations, but I can't go on. This is the first one http://img818.imageshack.us/img818/298/imageevsu.jpg This is the second one: http://img7.imageshack.us/img7/7812/imageowud.jpg Homework Equations The Attempt at a Solution...

Homework Statement cos(x-y)cosy-sin(x-y)siny=cosx a.try to prove that the equation is an identity b. determine a counterexample to show that it is not an identity Homework Equations cos(x-y) = cosxcosy+sinxsiny sin(x-y) = sinxcosy-cosxsiny The Attempt at a Solution a.Left side of...

Homework Statement Solve the differential equation: \frac{dy}{dx} = cos^2 (x) cos^2 (2y) The Attempt at a Solution I rewrote the equation \frac{dy}{cos^2 (2y)} = sec^2 (2y) = cos^2 (x) dx. Then I integrated, \frac{tan(2y)}{2} = \frac{1}{2} (x + sin(x)cos(x)) + c. Then I solved for y...

Homework Statement http://img35.imageshack.us/img35/806/imagezxg.jpg Homework Equations The Attempt at a Solution http://img853.imageshack.us/img853/4035/imageyffi.jpg

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

The problem is to solve the integral of : dx / (x^2(9-4x^2)^(1/2)) using trig substituition, which I really don't understand. Formula's that are useful: The integral table Integral 1/(u^2(a^2-u^2)^(1/2))= -((a^2-u^2)^(1/2)) / (ua^2) Work so far: Figuratively banging my head...

Homework Statement consider the function f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/)cosx+cos2x+cos3x+...+cos(n-1)x+cosnx) Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200 Homework Equations you get obviously tanx+tan2x...

Homework Statement find the value(s): cot(2sin^(-1) 2/7) The Attempt at a Solution I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came...

Homework Statement Not long ago I had a similar problem, which I was able to solve after reading this thread, but for this question I'm stuck and I could use a small hint. Homework Equations The Attempt at a Solution Thanks

1. Sin^2(x) = 3 – x Answer: 2.97 Attempts: 1-cos^2(x) = 3 – x cos^2(x) - x + 2 = 0 Factored it and got x = pi = 3.14 It’s a multiple choice question, and other answers were 3.02,3.09 which are few decimal places off so the answer must not be pi since it's not even a choice. Is the...

hi.. i came through a problem in which the expression [1-(k(sin^2) θ)] has to be simplified.. can someone help me to solve it.??

Homework Statement Find the derivative of: sqrt(x^2-4)-2tan^-1{.5*sqrt(x^2-4)} Homework Equations U'/1+U^2 U'=x/2sqrt(x^2-4) 1+U^2=x^2 The Attempt at a Solution I combined the above components but my answer is incorrect. I feel that I might have the wrong answer for...

Evalutate ∫ytan^-1(y) dy i don't know how to start, can somebody tell me how?

Hi everyone, Homework Statement My problem is just to derive a simple formula, which is http://www.texify.com/img/%5Cnormalsize%5C%21%28-1%29%5E%7Br%28r%2B1%29/2%7D%20%3D%5Csqrt%7B2%7D%20%5Cmbox%7Bcos%7D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%282r%2B1%29.gif Here r is a positive integer. The Attempt...

Homework Statement Find the derivative of f(x) = 1/4 sin^2 2x Homework Equations The Attempt at a Solution f'(x) =1/4(sin 2x)^2 f'(x) = 1/4*2(sin 2x)(cos 2x) f'(x) = 1/4(sin 4x) That is my answer to the problem, but the book has it as f'(x) = 1/2(sin 4x) What did I do...

Hello math helpers and others. Before I ask my question I would like to say that I appreciate everyone's help on these boards, and I hope that I will not be too large of a nuisance in the future. I am in my first calculus class, and it appears that I am going to need a lot of help. I was a...

Hello, do you have any strategy to suggest in order to solve the following system of partial differential equations in x(s,t) and y(s,t)? \frac{\partial x}{\partial t} = x - \frac{1}{2}\sin(2x) \frac{\partial y}{\partial t} = y \; \sin^2(x) (note that the partial differentiation is always with...

Homework Statement solve the following limit: \lim_{x\rightarrow0}\frac{x+sinx}{2x-sin3x}The Attempt at a Solution I know the principle of solving all sorts of limits but not trig limits, and since we just started trig limits it's still not clear to me, but i think to solve it we have to...

Homework Statement tan(\alpha)=\sqrt{2}-1 for every alpha in ]0,90°[ Homework Equations 1-count tan(2α) 2-conclude the value of α The Attempt at a Solution 1-after using tan(2α)=(2tanα)/1-tan^2α) i got tan(2α)=(√2-1)/2 2- I know that α is pi/8 but i just don't know how to...

Homework Statement cos 2x-cos^2 x=0 The Attempt at a Solution I have no idea.

Homework Statement I don't understand why the x/2 is not being integrated. I would think one should use u substitution. u = x/2, du = x, but they're not doing that.

I was messing around proving the area of a circle using trigonometric substitution. However, I ended up with area = -πr^2. In my integral I ended up using trigonometric substitution and setting x = r*cos(theta) However, this yields x = -r*sin(theta)*d(theta). When that's substituted...

Homework Statement I don't see how they're going from sec x cot x to csc x and csc x tan x to sec x The derivative of sec x is sec x tan x not csc x tan x and the derivative of csc x is -csc x cot x and if it's an identity then they didn't care to inform me of that at...

Homework Statement The question asks me to evaluate the indefinite integral: sin2x/(1+(cos2x)^2) The (cos2x)^2 is read cos squared 2x, i just don't know how to put the squared before the 2x and not have it look confusing ! Homework Equations The Attempt at a Solution To be...

Homework Statement I understand everything except why the derivative of 2 + tan (x/2) is .5 + sec^2(x/2) I don't understand the .5 part. I understand the sec part. I would think the derivative of 2 would be C, or just disappear.

Prove that: \[ \int_{0}^{\pi/2} \cos(nx) \cos^n(x) dx =\frac{\pi}{2^{n+1}}\] \[ \int_{0}^{\pi} \frac{1-\cos(nx)}{1-\cos(x)} dx =n\pi \] where \( n \in \mathbb{N} \). You can use induction, contour integration or any other method you like.

Homework Statement Tan^3Theta Homework Equations Tan^2Theta=1-cos2Theta/1+cosTheta The Attempt at a Solution Attached

Homework Statement Prove that (for every x smaller than -1) \displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}+arccotx=\pi Homework Equations The Attempt at a Solution So i split the formula into two parts: \displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}} and \displaystyle...

I found this question on a website. Homework Statement Prove that \displaystyle \int_{0}^{\pi}\frac{1-\cos(nx)}{1-\cos(x)} dx=n\pi \ \ , n \in \mathbb{N} 2. The attempt at a solution Here's my attempt using induction: Let P(n) be the statement given by...

Homework Statement arctan(8x-8)=-1 Homework Equations I'm sure what this part wants. The Attempt at a Solution tan[arctan(8x-8)]=tan(-1) 8x-8=tan(-1) x=(1/8)(tan(-1)+8) x=(1/8)(-(tan(1)+8) x= I am stuck on the last part since the homework says Simplify the above equation...

Homework Statement prove that for any integer n tannθ = ((n choose 1)tanθ - (n choose 3)tan^3θ + (n choose 5)tan^5θ)-.../ (( n choose 0) -(n choose 2)tan^2θ + (n choose 4)tan^4θ-...) The first 3 numbers on top and bottom look like these however the sum and differences keep going, and you...

Homework Statement basically i have this proof to do where (cot5x * [trigonometric function]5x)/csc6x = 5/6 and i have to prove it equals 5/6 Homework Equations but what i can't remember about the problem is the second function. I've tried plugging in all of them and using a made up value of...

Homework Statement [SIZE="7"]∫ (x+2)dx/√(4x-x2) Homework Equations why was the -2 in -2(x-2) was ignored? The Attempt at a Solution so first i let u= 4x-x2 then, du=4-2x = -2(x-2) so to get (x+2) i equate it to (x-2)+4 so ... [SIZE="7"]∫ (x+2)dx/√(4x-x2) =...

Hi, I have been representing complex numbers in graphical form in school recently. My teacher was telling me about a graph which shows all 4 quadrants and basically shows you what each quadrant is in terms of pi. Hopefully you understand what I mean, I have been looking on the internet for this...

any help with me understanding this problem would be very much appreciated. Homework Statement show, ^{π/2}_{0}\int cos^{5}xdx = 8/15 hence show ^{π/2}_{0}\int sin^{5}xdx = ^{π/2}_{0}\int cos^{5}xdx where, cos^{5}θ = \frac{cos5θ + 5cos3θ + 10cosθ}{16} sin^{5}θ = \frac{sin5θ -...

Homework Statement Finding the time derivative of sin^2( \alpha ), knowing that \dot \alpha ≠ 0 Homework Equations i know that \frac {d}{dt} sin ( \alpha ) = \dot \alpha cos ( \alpha) The Attempt at a Solution That should give \dot \alpha ^2 cos^2( \alpha ) But it's...

Homework Statement 2 ∫ dx / (x+1)√[2x(x+2)] 1 Homework Equations Let x = tan θ if √(a^2 + x^2) Where a = constant The Attempt at a Solution 2 ∫ dx / (x+1)√(2x)√(x+2) 1 2 1/√2 ( ∫ dx / (√x)(x+1)[√(x+2)] 1 Now make all x...

Where would be the best place to find every trigonometric identity, from sin[2] + cos[2] = 1, to the matrix identities (and Euler's equation would be helpful, also) Also the location of mathematical analysis symbols would be helpful, also. Thank you very much in advance :)

I'm self-studying Calculus and would like to ask some doubts about the following question: Homework Statement If, in t seconds, s is the oriented distance of the particle from the origin and v is the velocity of the particle, then a differential equation for harmonic simple motion is...