Trigonometric Definition and 1000 Threads

  1. MarkFL

    MHB Katlynsbirds' question at Yahoo Answers regarding inverse trigonometric identity

    Here is the question: Here is a link to the question: Prove the identity, pre calc!? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  2. anemone

    MHB Factoring Trigonometric Expression.

    Decompose the expression below into real factors: $$1-\sin^5 x-\cos^5 x$$
  3. A

    Solving Trigonometric Ratios: Finding cosx/cosy from sinx/siny

    i got sinx/siny=1.2 and i need to find cosx/cosy can i do it or maybe i need more knowledge?
  4. M

    Complex exponential to trigonometric simplification

    Homework Statement Given (e^(ix) - 1)^2 , show that it is equal to 2-2cosx Homework Equations e^ix = cosx + isinx The Attempt at a Solution After subbing in Euler identity and expanding I get: cos(x)^2+sin(x)^2-2cosx-2jsinx+2jcosxsinx + 1 after using the addtion formulas I get...
  5. anemone

    MHB Minimize the trigonometric expression.

    Find the minimum value of $$|\sin x+\cos x+\tan x+\cot x+\sec x+\csc x|$$ for all real numbers $$x$$.
  6. G

    Precalculus question using trigonometric equations

    Homework Statement Can you all help? The problem is 2 sin(x/2) - 1 = 0 I don't know what to do with the (x/2). The Attempt at a Solution So far I've done this: 2 sin(x/2)-1=0 2 sin(x/2)=1 sin(x/2)=1/2
  7. S

    Finding the sum of a trigonometric series

    1. The problem statement Find the sum of the series: a. 1 + a cos θ + a^{2} cos 2θ + a^{3} cos 3θ + ... + a^{n} cos nθ Apparently, the answer is: \frac{a^{n+1}(a cos nθ - cos(n+1)θ) - a cos θ + 1)}{a^{2} - 2a cos θ + 1} 2. The attempt at a solution = The real part of z^{0} +...
  8. S

    Trigonometric Identity Proof: v cosδ = V(1-cosβ) + u cos(α-β)

    Homework Statement Given the following two triangles: Show that v \cos{\delta} = V(1-\cos{\beta})+u\cos(\alpha - \beta) The Attempt at a Solution Using the cosine law I've got: v^{2}=x^{2}+V^{2}-2xV\cos{(\theta + \beta)} and u^{2}=x^{2}+V^{2}-2xV\cos{(\theta)} I figured maybe using the...
  9. D

    Trigonometric substitution in double integral

    Homework Statement Let R = \{ (x,y) \in \mathbb{R^{2}}: 0<x<1, 0<y<1\} be the unit square on the xy-plane. Use the change of variables x = \frac{{\sin u}}{{\cos v}} and y = \frac{{\sin v}}{{\cos u}} to evaluate the integral \iint_R {\frac{1} {{1 - {{(xy)}^2}}}dxdy} Homework Equations...
  10. anemone

    MHB Find x such that the given trigonometric expression equals zero.

    Find [FONT=MathJax_Math]$$x$$ such that trigonometric $$\dfrac{\sin (3x) \cos (60^{\circ}-x)+1}{\sin (60^{\circ}-7x)-\cos (30^{\circ}+x)+m}=0$$ where $$m$$ is a fixed real number. Hi all, I know the expression in the numerator has no real roots by checking it at W|A (plot the graph of...
  11. W

    Trigonometric Integrals Technique

    Homework Statement When integrating a function of the form: \displaystyle\int_c^d { (sinx)^{a} * (cosx)^{b}} Is this a correct simplification of the rules to evaluate: 1. if exponent on sin or cos is odd, and the other is even, separate out one of the odd's and use an identity on the...
  12. P

    Prove the trigonometric identity

    Homework Statement (question attached) Homework Equations The Attempt at a Solution Checking solution.. pretty sure I did this wrong. (solution attached)
  13. P

    Simplify Trigonometric Expression

    Homework Statement Simplify the following trigonometric expression: cscθtanθsecθ Homework Equations tanθ = sinθ/cosθ sin^2θ + cos^2θ = 1 cscθ = 1/sinθ secθ = 1/cosθ cotθ = 1/tanθ The Attempt at a Solution I just want to double check my solution. cscθtanθsecθ = 1/sinθ x...
  14. P

    How to Solve for θ When tan(θ) = 1 ± √2?

    I have shown the first part that they ask for. For the second part: let tanθ = t tan(3\theta) = \displaystyle\dfrac{tan(2\theta) + tan\theta}{1-tan(\theta)tan(2\theta)} = \dfrac{\frac{2t}{1-t^2} + t}{1 - t(\frac{2t}{1-t^2})} hence t = 2 + \dfrac{3t - t^3}{1-3t^2} t^3 - 3t^2 + t + 1...
  15. Feodalherren

    Differentiating trigonometric F'ns with double angles

    Homework Statement Sin(tan(2x)) With respect to x Homework Equations Differentiation The Attempt at a Solution My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ? Or do I have to convert to sine/cosine and go from...
  16. P

    Trigonometric Subsitution Integral

    Homework Statement ∫cot^2(x)csc^4(x)dx Homework Equations The Attempt at a Solution ∫cot^2(x)(cot^2(x)+1)csc^2(x)dx u=cot(x) du=-csc^2(x)dx -∫u^2 (u^2 +1)du -∫u^4 + 2u^3 + u^2 du -(u^5)/5 - (u^4)/2 - (u^3)/3 -cot^5(x)/5 - cot^4(x)/2 - cot^3(x)/3 + C Wolfram alpha shows the solution as...
  17. Petrus

    MHB Tangent lines of trigonometric functions

    Hello, I got problem with A homework "find an equation of the tangent line to curve at the given point. $y=sec(x)$. $(pi/3,2)$ progress: $y'=sec(x)tan(x)$. So basicly that sec(x) don't say me much so i rewrite it as $1/cos(x)$ $y'=1/cos(x)•tan(x)$ now i can put $pi/3$ on the function to...
  18. D

    Derivative of trigonometric functions

    Homework Statement g(x) = 4∏ [cos(3∏x) sin (3∏x)]The Attempt at a Solution g(x) = 4∏ [cos(3∏x) sin (3∏x)]' 4∏{[cos (3∏x)][sin(3∏x)]' + [sin(3∏x)][cos(3∏x)]'} = 4∏{[cos (3∏x)][cos(3∏x) . (3∏)] + [sin(3∏x)][-sin(3∏x) . (3∏)] = Now, my question is: Can I combine the numbers and have the...
  19. Petrus

    MHB Trigonometric functions: Sec, Cot, Csc

    Hello, Im currently on chapter about derivate trigonometric functions. It have been hard for me to understand this sec,cot,-csc? Why do you rewrite example $1/cos^2x$ as $sec^2x$? when I get like sec,csc etc i kinda feel i have no clue what it means. Then you think what do Petrus mean? example I...
  20. S

    Help with derivative of trigonometric functions

    Find y^{I} (sinxsecx)/1+xtanx The supplied answer is 1/(1+xtanx)^{2} I got stuck with an extra x on top at the end. Where did I mess up at? y^{I}(sinxsecx)/1+xtanx = [1+xtanx*f^{I}(sinxsecx)-sinxsecx*f^{I}(1+xtanx)]/(1+xtanx)^{2} =...
  21. W

    How do I evaluate this trigonometric integral involving cosine?

    Homework Statement evaluate the integral. Homework Equations integral (pi/6 to pi/4) [(sin2x)^4 / sqrt(1-cos2x) dx] The Attempt at a Solution 1. multiplying by conjugate: sqrt(1+cos2x)/sqrt(1+cos2x) . 2. should i split the (sin2x)^4 into (1-(cos2x)^2)^2 ?
  22. W

    Trigonometric Integral: Solving (5pi/6 to pi) (cosx)^4 / sqrt(1-sinx) dx

    Homework Statement solve the integral.Homework Equations integral (5pi/6 to pi) (cosx)^4 / sqrt(1-sinx) dxThe Attempt at a Solution Following the solution manual: integral (5pi/6 to pi) ( (cosx)^4 / sqrt(1-sinx)) * sqrt(1+sinx)/sqrt(1+sinx) however i am not sure how to do the algebra here...
  23. R

    Help with trigonometric substitution

    Homework Statement integral (1)/(x^2sqrt(36-x^2) Homework Equations The Attempt at a Solution I found X=6sinθ dx=6cos √(36-x^2)=√(36-sin^2θ)=6cosθ i think the problem is that i am not getting integral of ∫csc^2θ
  24. MarkFL

    MHB Rebekah's question at Yahoo Answers involving inverse trigonometric functions

    Here is the question: Here is a link to the question: Given 0<x<orequalto 1, determine the value of inversine (x) + inversetan (squareroot(1-x^2)/x)? - Yahoo! Answers I have posted a link there to this topic so the OP may find my response.
  25. A

    Trigonometric Integrals by Substitution

    I am unsure whether I have properly performed the integration of the integral ∫((sin(√x))^3*dx)/√x When I used my TI-Nsprire CAS to take the derivative of my answer in order to check if I was correct, and it came out differently. Now I used some trig identities to manipulate the problem, so I...
  26. D

    How can you evaluate a definite integral using trigonometric substitution?

    Homework Statement evaluate the definite integral ∫(0 to 3) dx/sqrt(25+x^2) Homework Equations The Attempt at a Solution I first used substitution and set x=5tanθ, and dx=5tanθsecθdθ then i wrote the integral as 5∫ tanθsecθdθ/sqrt(25(1+tan^2(θ)) after some simplification i...
  27. A

    Euler's Method of Trigonometric Series- Real Analysis

    Homework Statement Use Equation (1) to derive the formula: (1-a*cos(phi))/(1-2*a*cos(phi)+a^2))= 1+a*cos(phi)+a^2(cos(2phi))+a^3(cos(3phi))... Homework Equations Equation (1) is 1/(1-a(cos(phi)+isin(phi)))= 1+ [a(cos(phi)+isin(phi)]+ [a(cos(phi)+isin(phi)]^2 +...
  28. MarkFL

    MHB Mangoqueen54's question at Yahoo Answers involving a trigonometric identity

    Here is the question: Here is a link to the question: http://answers.yahoo.com/question/index?qid=20130130130636AAOqgvz I have posted a link there so the OP can find my response.
  29. Fernando Revilla

    MHB Katie's question at Yahoo Answers: trigonometric equation

    Here is Katie's question: Here is a link to the original question: Solve for x in the equation 1+sinx/cosx + cosx/1+sinx = 4 for 0 < x < 2pi? - Yahoo! Answers I'll post a link there to this topic so the OP can find my response.
  30. anemone

    MHB Have you tried using the double angle formula for cosine?

    [FONT=times new roman]Please consider the following equation: $\displaystyle \sum_{k=1}^{n}\cos^4\left(\frac{k\pi}{2n+1} \right)=\frac{6n-5}{16}$ [FONT=times new roman] For this particular equation, which I am trying to prove is true, I have found no way to crack it, even if I let $n=2$ and...
  31. T

    Trigonometric Inverse Substitution: How do we know which substitutions to use?

    If we see the form \sqrt { { a }^{ 2 }-{ x }^{ 2 } }, we always set x=asinθ How do we know that it will work in advance? Just trial & error?
  32. L

    MHB Proving a trigonometric equation

    I want to prove this equation: \cos\left(\frac{2\pi}{5}\right)+\cos\left( \frac{4\pi}{5}\right)+\cos\left( \frac{6\pi}{5}\right)+\cos\left(\frac{8\pi}{5} \right) = -1 . I've no idea how to begin. I think it may be related to complex numerd but I don't know how to combine them.
  33. P

    Trigonometric identities and complex numbers

    Homework Statement Show, using complex numbers, that sin(x)+cos(x)=(√2)cos(x-∏/4) Homework Equations cos(x)=(e^(ix)+e^(-ix))/2 sin(x)=(e^(ix)-e^(-ix))/2i e^ix=cos(x)+isin(x) The Attempt at a Solution I was given the hint that sin(x)=Re(-ie^(ix)), but have thus far not been...
  34. U

    Inverse trigonometric equation

    Homework Statement Solve cot^{-1} x - cot^{-1} (n^2 - x+1)=cot^-1(n-1) Homework Equations The Attempt at a Solution I can write the above equation as θ+α=β where the symbols represent the respective inverse functions. Now I take tan of both sides. Simplifying I get...
  35. T

    Trigonometric Laurent Series and Complex Integration

    My task is to solve the integral \frac{1}{\cos 2z} on the contour z=|1| using a Laurent series. The easy part of this is the geometric part. I drew a picture of the problem. I see that there are two singularity points that occur within the contour region at \pm \frac{\pi}{4}. I realize...
  36. S

    Hello,when I have to solve a trigonometric problem I can easily

    Hello, when I have to solve a trigonometric problem I can easily figure in my mind sin and cos, but how can I figure tan ?
  37. skate_nerd

    MHB Question about trigonometric substitution

    [FONT=arial]Studying for finals here...So I have this specific problem to use trig substitution on. $$\int \frac{x^2}{\sqrt{1-x^2}}\,dx$$ I begin by substituting $$x={sin{\theta}}$$ I am fine with doing everything up to the point where I have an answer for the integral in terms of...
  38. E

    Capitalising trigonometric functions

    I have always capitalised the first letter of my trigonometric functions, for example, writing Sinθ as opposed to the usual sinθ. Is it wrong to capitalise them? Does it make a difference in meaning?
  39. K

    How Do You Convert a Trigonometric Expression to a General Sine Function?

    Homework Statement Express the function f(x) = -2sin(3x) -4cos(3x) in the form of a general sine finction. Identify the amplitude, period, and phase shift Homework Equations sinx/cosx = tanx sin2x + cos2x = 1 The Attempt at a Solution don't know how to start don't...
  40. S

    Solving Trigonometric Equations with multiple solutions

    Homework Statement Solve each equation for solutions on the interval 0 ≤ x ≤ 2∏. 2 sin x = √3 The Attempt at a Solution Okay so I was able to solve this one: 2 sin x = √3 sin x = (√3) / 2 So i got x = ∏/3 ; 2∏/3 ; 4∏/3 ; 5∏/3 I substituted the x's into the original...
  41. S

    Exact Value of Trigonometric Equations

    Homework Statement Find the exact value of the given expressions. sin (2 sin-1 (4/5)) or sin (2 arcsin (4/5)) Just two different ways of writing it Homework Equations maybe The Attempt at a Solution I've only gotten this far: sin (2 arcsin (4/5)) = 2 sin (arcsin (4/5))...
  42. R

    Trigonometric Methods - Calculating impedance in rectangular and polar forms

    Homework Statement Given the equivalent impedance of a circuit can be calculated by the expression Z= (Z_1 Z_2)/(Z_1+ Z_2 ) If Z1 = 4 + j10 and Z2 = 12 – j3, calculate the impedance Z in both rectangular and polar forms. Homework Equations j2=-1 The Attempt at a Solution Z=...
  43. Z

    Trigonometric Integration / relationship between f(cosx) and f(sinx)

    Homework Statement Show that: ∫f(sin(x))dx = ∫f(cos(x))dx where each integral is over the limits [0, \pi/2], for a 'well behaved' function f. 2. The attempt at a solution I have tried relating sin(x) and cos(x) and somehow rearrange one of the integrals to look like the other. Since...
  44. S

    Trigonometric Solutions for tg(4x) = 1: Clarifying Doubts and Correctness

    Homework Statement tg(4x) = 1 The Attempt at a Solution I have a doubt about the part I have to add to the result, are these solutions correct ? 4x = 45° + n * pi x = 11,25° + n * (pi/4) Thanks
  45. K

    Solving a trigonometric equation

    Homework Statement Solve 2cos(x)^2 + 3cos(x) + 1 = 0 for 0 <= x <= 2pi Homework Equations Trigonometric equations, yadda yadda yadda. The Attempt at a Solution 2cos(x)^2 + 3cos(x) + 1 = 0 cos(x)(2cos(x) + 3) = -1 cos(x) = -1/(2cos(x) + 3) I then figured out that you get a solution when...
  46. Y

    MHB Solving Trigonometric Limit w/o L'Hospital Rule

    Hello, I need some help with this limit, I have no clue how to do this with the next constraint: No use of L'hopital rule... Thank you ! \lim_{x\to1}\frac{sin(x^{3}-1)}{x-1}
  47. H

    MHB Solving a Trigonometric Equation

    2Cos (3/10x) - 3Sin(1/2x)=0 How would I go about solving this equation? I do not even know where to begin.
  48. M

    MHB Solving a Trigonometric Equation for Cos (x)

    Hi, may you help me? I have a question I solved but couldn't ended. If cos(x)+5Sec(x)=1.1 then Cos(x)=? 2Cos(x)+5Sec(x) =11/10 2Cos(x)+5/Cos(x)=11/10 2Cos(x)*Cos(x)+5=11/10*Cos(x) 2Cos^2(x)+5=11/10*Cos(x) 2Cos^2(x)-11/10-Cos(x)-5=0 then i used delta=b^2-4ac then i found delta=-4.79...
  49. M

    MHB Finding the Range of a Trigonometric Function

    Hello, I have some questions and i couldn't solve them can you help me? If y=5cos(x)+3 then what is the heap of ? (a) All real numbers (b) alpha<= y <= alpha (c) -2 <= y <= 10 ( d)-2 <= y <= 8 What is the solution? Thank you.
  50. T

    Solving Equations Using Trigonometric Identities

    Hey PF! Homework Statement Find exact solutions for the following equations over the domain 0 ≤ x <2π 2sinx = 3 + 2cscx Homework Equations sin2+cos2=1 The Attempt at a Solution 2sinx = 3 + 2cscx 2sinx = 3 +2(1/sinx) sinx = 3/2 + 1/sinx sinx - 1/sinx = 3/2 (1-1-cos2x)/sinx = 3/2 -cos2x/sinx =...
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