Trigonometric Definition and 1000 Threads

  1. 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...
  2. 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}
  3. 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.
  4. 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...
  5. 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.
  6. 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 =...
  7. D

    MHB Simplification of Trigonometric Expression

    $$ \cos[k_n(L-\varepsilon)]-\cos k_nL $$ I just read this for small epsilon this result can be further simpli ed by using the trigonometric identity for $\cos[k_n(L-\varepsilon)]$. Doing so result is $$ 2\sin k_nL $$ I don't see this? Can someone explain?
  8. T

    MHB Solving a Trigonometric Equation

    solve for tan^4x + tan^2x = sec ^4x - sec^2x i solved and ended up with RIHS= tan^4x?
  9. A

    Trigonometric function and complex exponential

    1. Homework Statement - multiplication of trigonometric function and complex exponential 2. Homework Equations the question is, Akcos(ωt) × e-jωt 3. The Attempt at a Solution it is, Ak/2 + (Ak/2)e-j2ωt ? by using cos(ωt) = 1/2ejωt + 1/2e-jωt
  10. M

    How Do You Solve an Integral Using Trigonometric Substitution?

    Homework Statement Hi I need help with the following integral. \int_0^2 \! \frac{1}{(x^2+4)} \, dx Homework Equations I believe that these are both trigonometric substitutions. However, these are the simplest in my textbook and I can't even understand them. :-( The Attempt at a Solution...
  11. K

    Trigonometric Identity Problem

    Homework Statement Prove the Identity sinθ/(1+cosθ) = 1-cos(θ)/sinθ Homework Equations sinθ/cosθ = tanθ sin^2θ + cos^2θ = 1 The Attempt at a Solution sinθ/(1 + cosθ) = LS cosθtanθ/(1+cosθ) = LS cosθtanθ/(sin^2θ + cos^2θ + cosθ) = LS cosθtanθ/(tan^2θcos^2θ +...
  12. alane1994

    MHB Area between two trigonometric curves.

    http://www.mathhelpboards.com/f12/im-clueless-how-start-2322/My math class uses an online homework system. I got the answer wrong to the question, but I can get a similar question. Here is one that is similar to the earlier one. You have two functions that are graphed. y=\frac{\csc^2{x}}{4}...
  13. alane1994

    MHB Solving a Trigonometric Equation

    I have this as part of a calculus problem. I guess I am a little rusty on this. Any help would be appreciated. 4\cos^2{x}=\frac{\sec^2{x}}{4} I believe that I need to solve for cosx. And then determine what cosx is in radians. That should be the lower limit of the integration. I know how it...
  14. M

    Some trigonometric, exponential thing?

    How can we say: f(x)=A'sin(kx)+B'cos(kx) or equivalently f(x)=Ae^{ikx}+Be^{-ikx}?? How are these two equivalent knowing that e^{ix}=cosx+isinx I don't get this?
  15. F

    Solving Trigonometric integrals using cauchy residue theorem

    Homework Statement evaluate the given trigonometric integral ∫1/(cos(θ)+2sin(θ)+3) dθ where the lower limit is 0 and the upper limit is 2π Homework Equations z = e^(iθ) cosθ = (z+(z)^-1)/2 sinθ = (z-(z)^-1)/2i dθ = dz/iz The Attempt at a Solution after I substitute and...
  16. F

    Summation of a trigonometric series

    Homework Statement Find the limit of the series \lim_{n \rightarrow \infty} \sum_{i=1}^{n} cos (i \theta / n) , 0≤θ≤π/2 Homework Equations The Attempt at a Solution I know that the expansion looks like \cos \theta / n + cos 2 \theta / n + ... + cos \theta , but I couldn't begin...
  17. O

    Solving a general complex trigonometric equation

    Hello everyone! Homework Statement Solving a relatively general equation representing a constant combination of 2 trigonometric functions.Homework Equations a\cos{(vx+p)}+b\cos{(ux+q)}=cThe Attempt at a Solution I really don't have any idea for a general solution to this equation.. Best Regards
  18. Z

    Trigonometric Function Homework: Satellite Orbit Calculations

    Homework Statement A satellite follows a path that may be modeled by the function H(t)= 350 sin 28∏(t-25) + 400 Time is measured in days. Homework Equations The Attempt at a Solution A) Determine the period of the satellite: 2∏*1/28∏ = 1/14 days B) How many minutes will it...
  19. Feodalherren

    Trigonometric Identity Homework: Solving with Sin and Cos Formulas

    Homework Statement Homework Equations Any trig formulas The Attempt at a Solution The yellow paper is me switching everything to sin and cos to see if that helps but it doesn't. I'm completely stuck here.
  20. Feodalherren

    Trigonometric Equation: Solving Sin 2x = -2cos x in the Interval 0 ≤ x < 2∏

    Homework Statement All solutions in the interval 0 ≤ x < 2∏ Sin 2x = -2cos x The Attempt at a Solution I went about it in two different ways. The first way: I simply used the double angle formula to get 2sinx cosx + 2cos x = 0 From this we get that whatever makes cos x = 0...
  21. Z

    Dumbfounded by this trigonometric equation.

    Homework Statement A beach ball is riding the the waves near Tofino, BC. The ball goes up and down with the waves according to the formula h= 1.4 sin(∏t/3), where h is the height in meters above sea level, and t is the time in seconds. A) In the first 10s when is the ball @ sea level. B)...
  22. M

    Simplifying a trigonometric product

    Was just double checking if we can simplify this in the following way, ∫ sinx * √(1 + cos2x) dx = ∫ sinx * (1 + cosx) dx
  23. K

    How to write powers of inverse trigonometric functions?

    Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?
  24. J

    Is there a known formula for integrating cos^5x sin^5x?

    ∫cos^5 x sin^5 x dx I thought I would try to solve this by first doing: ∫(1 - sin^2 x) cos^3 x sin^5 x dx but would like to know if that's right. [Edit] Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?[Edit]
  25. R

    Trigonometric substitution. Pretty confused where constant comes from. (fixed)

    Find ∫from .6 to 0 x^2/ sqrt(9-25x^2) dx My teacher worked this on the board a little confused O obviously the trig sub is asintheta. But it isn't in the right form yet. So get it there you pull out a 25 --) sqrt(25(9/25) - x^2 ) 5sqrt((9/25)-x^2 so x= (3/5) sintheta so dx = 3/5costheta. so...
  26. M

    Signs of the trigonometric functions of the angle -200

    Determine the signs of the trigonometric functions of the angle -200° in standard position. sin(-200°) cos(-200°) tan(-200°) csc(-200°) sec(-200°) cot(-200°) Information: Q1= (All Positive) Q2= (sin csc) Q3= (tan cot) Q4= (cos sec) Answer: sin(-200°) = Positive cos(-200°) =...
  27. M

    Values of the six Trigonometric Functions

    Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side is containing the points (-3,0) Sinθ= Cosθ= Tanθ= Cscθ= Secθ= Cotθ= I believe the following are correct But I am not sure, Please give insight Sinθ= 0/3 Cosθ= -3/3 Tanθ= 0/3...
  28. B

    Limits Involving Trigonometric Functions (identities)

    Does anyone know of websites where I can find many problems on the topic in the title line (my textbook has far too few)? Thanks!
  29. R

    Trigonometric Methods, using instantaneous value of current

    Homework Statement The instantaneous value of current, i amp, at t seconds is given by: i = 15 sin(100π.t + 0.6) Find the value of; a) amplitude b) period c) frequency d) initial phase angel e) value of i when t = 2.5s f) time when current first reaches maximum value Homework...
  30. P

    Trigonometric Equations Solution

    Hi, I had to solve without the aid of a calculator: 2cos(x) = sin(2x) What I did was perform the following substitution: 2cos(x) = 2sin(x)cos(x) I then canceled and got: sin (x) = 1 For 0 to 3pi, I got two answers, pi/2 and 5pi/2. I did not get one of the answers. Why...
  31. A

    Trigonometry Word Problem involving Inverse trigonometric functions

    Homework Statement A ship is d feet from a dock (horizontal distance). The dock is 40 feet above sea level. The angle of depression from the dock to the ship is θ. Write θ as a function of d. Homework Equations This question is accompanied with choices. The choices are (A) θ = 40arctan(d) (B)...
  32. A

    Solution of Trigonometric Equations

    Homework Statement Find the solution set of each of the following equations for the interval 0° ≤ x ≤ 360°. sin^2x = sinx Homework Equations Trigonometric Identities for Sine. The Attempt at a Solution This is my attempt so far: \sin^2x = sinx \sin^2x - sinx = 0 \sin^2x - sinx + \frac{1}{4}...
  33. A

    Finding x in an inverse trigonometric equation

    Homework Statement Given y = 2/3(arctan \frac{x}{4}), find x. Homework Equations Inverse trigonometric identities for tan. (I guess)The Attempt at a Solution I never attempted because it seems impossible for me. You think this is possible? Thank you!
  34. A

    A question about trigonometric identities

    Is this identity possible? cot 2x = \frac{cos3x + cosx}{sin 3x + sinx} Thanks!
  35. A

    Why Does arccos(x) - arcsin(1-x) Equal 90° Have No Solutions?

    Homework Statement Find the solution set of the equation below for the interval 0° ≤ x ≤ 360°: arccos(x) - arcsin(1-x) = 90° Homework Equations all given above. The Attempt at a Solution i tried to consider (1-x) as "complementary" but I'm not really sure about that and I would...
  36. A

    Proving Trigonometric Identities problem

    Homework Statement Verify that \frac{cosθ}{1-tanθ} + \frac{sinθ}{1-cotθ} = sinθ + cosθ is an identity.Homework Equations - Reciprocal Trigonometric Identities - Pythagorean Trig IdentitiesThe Attempt at a Solution Every time I try to manipulate the LHS of the equation I always get -1 and as far...
  37. A

    Proving Trigonometric Identities

    Homework Statement Prove that sin6 + cos6 = 1 - 3sin2cos2 Homework Equations (1) The Attempt at a Solution I tried to convert those all in terms of sine and cosine only but it didn't work.
  38. A

    Inverse Trigonometric Equation problem

    EDIT: 1.Homework Statement The problem asks to simplify this: cos(arcsin x)Homework Equations let arc sin x = θThe Attempt at a Solution EDIT: I have to edit because I received a warning for not posting for #3 and #2. I originally posted "cos(arcsin x)" for #2 because that was what I know...
  39. P

    Trigonometric Limit Problem: Finding the Limit as x Approaches 0

    Homework Statement find the limit as x approaches 0 of 3sin4x / sin3x Homework Equations sin2x = 2sinxcosx lim as x ->0 of sinx / x =1 The Attempt at a Solution sin4x = 2 sin2x cos2x
  40. D

    Proving trigonometric identities

    Homework Statement Prove that: (1-tanθ)/(1+tanθ)=(cotθ-1)/(cotθ+1) Homework Equations Trig Identities: tanθ= sinθ/cosθ cotθ= cosθ/sinθ 1+tanθ=secθ 1+cotθ=cosecθ The Attempt at a Solution These sorts of equations are coming up a lot and I am having trouble understanding...
  41. S

    Trigonometric integration question

    The question asks to find ∫secxtan2x I rewrote tan2x as (sec2x-1). Then I expanded the equation having sec3x-secx and I know the integral of secx which is 0.5ln|tanx+secx|, but my question is, is integrating sec3x by parts the correct path? or not? Thanks
  42. S

    Help with trigonometric integration problem

    The problem is to find \int(cos5x)/(\sqrt{sinx}) I rewrote cos5x as cosx(1-sin2x)2, finally getting: (cosx-2cosxsin2x+cosxsin4x)/\sqrt{sinx} and I don't even know if this is the correct path, so, any advice would be appreciated.
  43. D

    Trigonometric identities hard question

    Homework Statement Simplify the following: sin(b)/cos(b) + cos(b)/sin(b) Homework Equations Trigonometric identities The Attempt at a Solution Ok so i have no clue how to do this,I keep trying but can't seem to get the right answer, I have tried to do this: sin(b)/cos(b) +...
  44. L

    Solutions of trigonometric equations

    [b]1. The problem statement: QUESTION:the general solution of equation (√3 - 1)sin∅+(√3 + 1)c0s∅=2 is 1) ∅=2nπ+- (π/4)+(π/12) 2) ∅= nπ + (-1)^π (π/4)+(π/12) 3) ∅=2(n+1)π (π/4)+(π/12) The Attempt at a Solution ACTUALLY I DONT NEED THE ATTEMPT, i know the answer is option 1 , i don't...
  45. S

    MHB Help on Trigonometric sums. (Assorted type)

    I have some questions and doubts in trigonometry. I hope somebody can solve these questions. Q1) If for real values of x, cos\theta = x +\frac{1}{x}, then a) \theta is acute angle b) \theta is right angle c) \theta is an obtuse angle d) no value of \theta is possible I will post the following...
  46. J

    MHB Number of Real Solutions for Trigonometric Equation

    Number of real solution of the equation $\sin (\sin (\sin x)) = \cos (\cos (\cos x))$ where $ 0 \leq x\leq 2\pi$
  47. M

    Solving Trigonometric Equations: sin(θ) = 3/5

    Spending my summer studying on my own, and I have come across some things which I would like to see how they are solved. If you are capable of completing, please show work instead of just answers so that I can follow what you did, and take notes on it. Homework Statement If sin(θ) =...
  48. H

    Limit of a trigonometric integral

    Homework Statement Excersice of Big Rudin: ch. 4, prob. 9. If A\subset [0,2\pi] and A is measurable, prove that \lim_{n\to\infty}\int_{A}\cos\,nx\,dx=0 Homework Equations Bessel's inequality The Attempt at a Solution I give my solution, but I post because I think that my answer...
  49. J

    Proving the trigonometric identity

    Homework Statement To prove that \sum over m=1 to 15 of sin(4m-2) = 1/4sin2, where all angles are in degress Homework Equations The Attempt at a Solution Tried to solve it using identity sinx+siny=2sin((x+y)/2)cos((x-y)/2)..but all attempts failed..help
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