Trigonometric Definition and 1000 Threads

  1. D

    Limit proof of trigonometric function

    Homework Statement Prove that limh→0[(cos(h-1))/h]=0. Homework Equations Half angle formula From an example: limh→0[(cos(h-1))/h] = limh→0[-(2sin2(h/2))/h] They state that they use the half-angle formula in the following way: cosh= 1-2sin2(h/2) I'm not really sure how they are getting...
  2. M

    MHB Question about Trigonometric Substitution

    Hello again, I have a question about a trigonometric substitution problem that I am struggling with. I was able to get the correct answer, which I know is correct because of Wolfram verification, and my school has a way of showing an example which showed the steps... Anyway, see below...
  3. S

    Heiseinberg's Microscope - Trigonometric and Interpretation questions

    Homework Statement The problem along with its solution is attached as ProblemSolution.jpg. Homework Equations Δx = λ/sinθ (Eq. 1) Δp_x = (h/λ)(sinε) (Eq. 2) The Attempt at a Solution In Wikipedia, I found this article: http://en.wikipedia.org/wiki/Heisenberg's_microscope which uses...
  4. S

    How Do You Solve the Integral of sin^3(x)cos^6(x)dx?

    Homework Statement ∫sin^3xcos^63xdx Homework Equations The Attempt at a Solution ∫sin^3xcos^63xdxsin^3xcos^63xdx let u=cosx du=-sinxdx -du=sinxdx =∫sin^2xcos^63xsinxdx =∫(1-cos^2x)cos^63x-du =-∫(1-u^2)u^63du =-∫(u^63-u^65)du =-u^64/64-u^66/66+c...
  5. M

    MHB Can You Help Me Solve This Trigonometric Integral?

    Hello again. I am hoping that someone can assist in checking my work regarding a trigonometric integral. The problem and my attempt to solve is as follows. \int\sin^{\frac{-3}{2}}(x)*cos^3(x) dx \int\sin^{\frac{-3}{2}}(x)*cos^2(x)*cos(x) dx Using a Pythagorean identity...
  6. H

    Proving this trigonometric identity

    Homework Statement Show that : 1 + cos(2∏/5)= 2 cos(∏/5) Homework Equations cos(2x) = cos^2(x)-sin^2(x) cos^2(x)+sin^2(x) = 1 The Attempt at a Solution I have tried using the two formulas above but i couldn't show the required result.
  7. M

    Dif.eq. with trigonometric functions involving y

    I tried to solve it but confused. Pls. help me to solve this equation: dy/dx + (e^x)*Sec(y) = Tan(x); (hint: integrating factor is e^-ax, and a is unknown, a ε ℝ, find it, solve the equation) Thnx.
  8. I

    Substituting Integration with trigonometric function

    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...
  9. M

    Trigonometric Integration: Solving ∫ dx/√(1-k*sin2x)

    Hi everyone, In my research project, i am struck with an integration. Can someone help me out: ∫ dx/√(1-k*sin2x) Thanks, Sandeep
  10. K

    Algebraic proofs of trigonometric identities

    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...
  11. A

    Converting Trigonometric Ratios to Degree

    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...
  12. J

    Trigonometric Identity: Double Angle.

    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...
  13. S

    MHB Need Help With a Trigonometric Equation?

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

    Can Trigonometric Identities Be Proven Using Different Methods?

    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.
  15. S

    Limit of a trigonometric function without l'hopitals rule?

    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...
  16. D

    Difficulty to find this limit of trigonometric function

    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...
  17. cocopops12

    How can someone prove the following trigonometric identity?

    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)
  18. J

    Trigonometric form of Legendre equation

    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...
  19. O

    Trigonometric Equations - Why Do I Always Get cos^3 or sin^3?

    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...
  20. E

    Prove trigonometric identity and determine a counterexample

    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...
  21. T

    Differential Equation Involving Trigonometric Functions

    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...
  22. O

    What Steps Are Needed to Solve This Trigonometric Function?

    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
  23. cocopops12

    What is the trigonometric identity used to simplify this expression?

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

    Trigonometric substitution dx / (x^2(9-4x^2)^(1/2))

    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...
  25. N

    What Values Make f(23,x) Equal to f(33,x) for 100<x<200 Degrees?

    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...
  26. D

    Trigonometric equations with sin and cot

    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...
  27. J

    Write the trigonometric expression as an algebraic expression

    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
  28. I

    Few Trigonometric Functions that I can’t solve involving identities? helpp

    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...
  29. P

    How can I simplify [1-(k(sin^2) θ)] using trigonometric identities?

    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.??
  30. B

    Derivative involving inverse trigonometric functions

    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...
  31. A

    How to solve ∫ytan^-1(y) dy using integration by parts?

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

    Derivation of a formula with trigonometric functions

    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...
  33. B

    Derivative of A Trigonometric Function

    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...
  34. M

    MHB SE BoardHow Can I Solve This Trigonometric Limit Problem?

    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...
  35. mnb96

    System of two differential equations with trigonometric functions

    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...
  36. M

    How to Solve Trigonometric Limits Using l'Hopital's Rule

    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...
  37. M

    Trigonometric Equation: Solving tan(\alpha)=\sqrt{2}-1 for \alpha in ]0,90°[

    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...
  38. lep11

    Mastering Trigonometric Equations: Solving cos 2x-cos^2 x=0

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

    Integrating x/2: Why is u-substitution not being used?

    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.
  40. B

    Troubleshooting Trigonometric Substitution for Circle Area Calculation

    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...
  41. B

    Understanding Trig Identities and Variations

    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...
  42. J

    Trigonometric Integral: Evaluating sin2x/(1+(cos2x)^2)

    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...
  43. B

    Why Does the Derivative of 2 + tan(x/2) Include a .5 Term?

    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.
  44. S

    MHB Can you prove this result for any $m,n\in\mathbb{Z}^+$?

    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.
  45. G

    Problem with using Power-Reducing Trigonometric identities

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

    Trigonometric proof using derivatives

    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...
  47. Blandongstein

    Integral involving trigonometric functions.

    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...
  48. C

    Inverse Trigonometric Problem Solve equation for x

    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...
  49. N

    Intense trigonometric question

    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...
  50. M

    What is the missing function in this trigonometric proof?

    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...
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