Trigonometric equation Definition and 133 Threads

  1. X

    Trigonometric Equation problem

    I'm stuck on a question from my calculus homework...T_T Here's the question... There is a large clock at the front of the lounge on the paddle steamer. The hour hand is 28 cm long and takes 12 hours to rotate once. At 2 o'clock the tip of the hour hand is 195 cm above the floor. There's...
  2. T

    Solving trigonometric equation

    This is part of the identity proving question . from \sin C=\frac{2}{\sqrt{29}} , how can i reach C=\frac{1}{2}\sin^{-1} (\frac{20}{29}) ?
  3. I

    Trigonometric Equation: Solve for x on Real Numbers Set | Homework Statement

    Homework Statement cos(x)+2tg(x) = 7/(4*cosx(x)) Solve for x on the real numbers set. Homework Equations tg(x) = sin(x)/cos(x) , cos^2(x) = 1-2*sin^2(x) , The determinant is D = b^2 - 4ac , Also cos(x) ,tg(x), sin(x) | -1 < x < 1 The Attempt at a Solution For final arrangement I...
  4. P

    Solving a Trigonometric Equation to Hit a Moving Target

    So the orginial question asked what angle to fire a gun to hit a moving target, and i got all the way to 40sinθcosθ-10sinθ-1 = 0, but we aren't supposed to use calculators so how would you solve this by hand. Thanks!
  5. C

    Solve x: Trig Equation (4/3)sinXcosX-sin22X=0

    Homework Statement Solve for x. x is greater than or equal to 0 and x is less than or equal to 2pi. (4/3)sinxcosx-sin22x=0 If there is a better way to approach this question than the way I did it below, please post it. Thanks.Homework Equations N/A The Attempt at a Solution...
  6. K

    How can I solve these trigonometric equations?

    Homework Statement The original problem is this: ab^2*cos(2x)*(cos(x))^2 + ba^2*sin(2x)*(sin(x))^2 = 0 And some of the more "logical" forms I've got to are these:2[tan(x)]^3-2tan(x) = -b/a tan(2x)*(tan(x))^2=-b/a But I can't solve these equations so I'd like to ask for some help here.
  7. James889

    Solving Trigonometric Equation with Cosine and Sine Identities

    Hi, I would like som help on this one: Give all the real soulutions to the equation \frac{7}{4}-2sin(x) - cos^2(x) = 0 i tried the common identities, like replacing cos^2(x) with 1-sin^2(x) any ideas?
  8. T

    Another Trigonometric Equation

    Homework Statement Solve for t sin3tcost+cos3tsint=-1/2 Homework Equations Sum and Difference Identities The Attempt at a Solution I saw this problem the the sum identity sin(\alpha+\beta) looked like the way to begin solving for t. This condenses to sin(3t+t)= -1/2 which...
  9. A

    Solving simultaneous trigonometric equation

    how to solve eqn1 = sin((alpha)*a)*cosh((alpha)*b)=sin(alpha)*a eqn2 = sinh((alpha)*b)*cos((alpha)*a) = b*sin(alpha) alpha = 0 to 2pi... Find a & b... Plz help me with any method that would help solving this...
  10. X

    Solving a Trigonometric Equation: (cos x)^4 = cos (x^2)

    Hi all, I was tutoring someone in Algebra III today and encountered a problem that threw me for a loop. (cos x)^4 = cos (x^2) Is there a way to solve this algebraically?
  11. L

    Simplify trigonometric equation problem

    Homework Statement Simplify the following. Write all trigonometric functions in terms of t. Homework EquationsThe Attempt at a Solution I know that: sec(t+2pi)=sec(t) 1+tan(t+3\pi)= 1+tan(t) What about: csc(t-6\pi)? Will it be equal to csc(t). Can anyone please help me with this? Thank you...
  12. A

    How Do You Solve Trigonometric Equations Involving Cosine and Sine?

    Hi All, I’m currently attempting to work ahead on my precalculs and I’m looking at trigonometric equations. I seem to have a bit of a problem with this example (i haven’t had too many issues with the rest of the exercises), 9cos(2x)+sin(x)=9 (solve for x in the interval 0 <=x <=2pi.) I’m...
  13. I

    Trigonometric Equation with Multiple Functions and Arguments

    Can anyone help solve the below for 'a' 0=b(ycos(a)-bcos(2a)+xsin(a)) I've reduced it to b=ycos(a)+2sin(a)sin(a)+xsin(a) =sin(a)(cot(a)+2sin(a)+x) Which I think is right, but I can't get any further without just ending up with different forms that appear more complex.
  14. N

    Solving trigonometric equation

    Hi guys, I need to solve the following trigonometric equation. Some time ago I would have used Fortran with the appropriate libraries but now I was wondering whether there is any better approach. Any suggestion? w^2/c^2= k//^2 - Sqrt(w^2 Eps_b^2/c^2 - k//^2) * Tan[Sqrt(w^2 Eps_b^2/c^2 -...
  15. M

    Solving a trigonometric equation help

    Homework Statement sqrt3 cot 3x + 1 = 0 where 0 _<x_<2pie Homework Equations The Attempt at a Solution I narrowed it down to a constant on one side, cot 3x = -1/sqrt3 which I could turn into cos x/sin x = -1/sqrt3 but I have no idea where to go from here. Any help...
  16. A

    Solving a trigonometric equation

    I'm trying to solve: sin2x = -cos2x so my first step was... 2sinxcosx = -cos^2x - sin^2x and then... 2sinxcosx + cos^2x + sin2x = 0 but I'm confused on how I would end up factoring 2sinxcosx + cos^2x + sin2x, or if I did something wrong earlier in the problem...thank you
  17. S

    Trigonometric Equation problem

    Homework Statement If cos x = a/b and tan x = c/d; where a, b, c do not equal 0, then sin x is... (a) bd/ac (b) bc/ad (c) ad/bc (d) ad/bc Homework Equations The Attempt at a Solution The way I see it, if cos x = a/b, then b=hypotenuse. if tan x = c/d, then d=...
  18. I

    Exact value of Trigonometric 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.
  19. H

    Help solving trigonometric equation?

    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.
  20. P

    Draw the triangle with sides 1, 3, and sqrt(10)

    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}...
  21. T

    Can You Solve This Trigonometric Equation 2 Homework Problem?

    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...
  22. I

    Fairly basic trigonometric equation

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

    Solving a trigonometric equation

    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...
  24. S

    Proving trigonometric equation?

    for x between 0 and 2pie, solve cos(4x)=sin(2x)... is this a proving trigonometric equation? i don't think it is
  25. J

    PLease HELP with this trigonometric equation

    Greetings my friends: I have been reading a book about optimization and I found the following trigonometric equation: tan(10x.pi)= - 10 pi x (this equation goes from x E [-1,2] it is easy to see that has infinite solutions, but the author came to the conclusion that the solutions are...
  26. C

    Complicated trigonometric equation

    I need to solve sin(ax)sin(bx) - k cos(ax)cos(bx) = -1 where k > 1 is constant and so are a and b, and they are all irrational. (It's part of a much larger question in optics...) Any ideas, please? Thanks
  27. S

    Factoring trigonometric equation

    Hi, I'm having trouble understanding how my math book factored the following equation. [(cos(t)sin(t) - (1 + sin(t))cos(t)) / (cos(t)cos(t) - (1 + sin(t))sin(t))] to get [(cos(t)(1+2sin(t))) / ((1 + sin(t)) (1 - 2sin(t)))] I get the numerator but I don't understand what happened...
  28. P

    Can this trigonometric equation be solved for x_1 and x_2 in terms of \alpha?

    x_1(cos\alpha-1) + x_2sin\alpha = 0 x_1sin\alpha + x_2(-cos\alpha-1) = 0 How to solve this equation? Can anyone help me?
  29. A

    Derive a trigonometric equation for the volume of the cone

    A circular cone is inscribed in a sphere with a radius of 30cm. The semi vertical angle is theta. Derive a trigonometric equation for the volume of the cone. This has be stumped. I tried looking up proofs for the expression of the volume of a cone for inspiration but all involve calculus.
  30. C

    Solving a Trigonometric Equation: Primary to Secondary Solutions

    How do I get from the primary to the secondary solution of a trigonometric equation? This book tells me that the second angle is within -\pi \leq \theta \leq \pi, in a different quadrent, but I don't follow :\ Thanks. Edit: I got it (I think!): I can pick the correct quadrent using the...
  31. N

    Solving a Trigonometric Equation

    How would you solve for \alpha in the following equation? 4=\cos(\alpha)+\cos^2(\alpha)+\cos^4(\alpha)
  32. C

    How do I solve a trigonometric equation on a given interval?

    Hello all Just refreshing in maths, and want to know if I am doing this correctly: Solve the equation \sin x = 0.2 on the interval 0 \leq x < 2\pi . I took \arcsin(0.2) , however how do you solve for all solutions in the interval? (i.e what if the interval had been 0 \leq x < \pi...
  33. J

    How to Solve a Trigonometric Equation with Multiple Solutions?

    How to solve this equation: tan 2x + sec 2x = cos x + sin x where 0<=x<=360 I solve it in this way but cannot find the right answer: (sin 2x + 1) / cos 2x = cos x + sin x (cos x + sin x)^2 / cos 2x = cos x + sin x (cos x + sin x) / cos 2x = 1 sqrt(2) cos(x - 45) sec 2x = 1 sec 2x cos(x -...
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