Trig Equation

posted by .

Solve for x (exact solutions):

sin x - sin 3x + sin 5x = 0

-¦Ð ¡Ü x ¡Ü 0


Now, using my graphics calculator, I discovered that the following equation has 5 solutions. I have managed to come up with 3 of them but I'm having trouble finding the other 2. My 3 answers are:

0, -¦Ð/6, -5¦Ð/6

I need the answers to be EXACT like above so any help would be appreciated. Thankyou.

  • Trig Equation -

    I answered this question two days ago. Once of the answers is of course x = 0. For the others, I substitued indentities for sin 3x and sin 5x in terms of sin x, and ended up with a factorable equation for sin x. This leads to exact equations for arcsin in terms of fractions.

    I am not able to read your terms -¦Ð/6 and -5¦Ð/6

    If I can find my original answer, I will post a link to it below

  • Trig Equation -

    OK, I found my original answer at
    and it has two mistakes, a missing exponent and an incorrect sign. I should have ended up with the equation
    3sinx - 16 sin^3x + 16sin^5x = 0
    which factors to
    sinx (3 - 16sin^2x + 16sin^4x) = 0
    sinx (4sin^2x-3)(4sin^2x -1) = 0
    Thge roots, besides x=0, are:
    sin^2x = 1/4
    sin x = +/-sqrt(1/2)
    sin^2 = (3/4)
    sin x = +/-(sqrt3)/2

  • Trig Equation -

    Any positive or negative integral multiple of 30 degrees (x=pi/6), including 0 degrees, satisfies the equation.

  • Trig Equation (correction) -

    All +/- integral multiples of pi/6 EXCEPT multiples of pi/2 are solutions

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
  2. trig

    find the exact solutions (è in degrees) sin^2è+2cosè=-2 change the sin^2 to 1-cos^2, then rearrage the equation into quadratic form, use the quadratic equaion.
  3. math

    Eliminate the parameter (What does that mean?
  4. Math (Trig)

    Solve the equation for exact values of x. sin(x) = 1-2(sin(x))^2
  5. Maths

    Solve for x (exact solutions): sin x - sin 3x + sin 5x = 0 ¦Ð ¡Ü x ¡Ü ¦Ð ---------------- Thankyou. I tried find the solutions on my graphics calculator but however, the question is to find the EXACT solution(s) for the equation …
  6. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
  7. Precalculs

    I have no idea how to do these type of problems. -------Problem-------- Solve each equation on the interval 0 less than or equal to theta less than 2 pi 42. SQRT(3) sin theta + cos theta = 1 ---------------------- There is an example …
  8. MathsSs triG

    Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-360)sin(90-x)tan(-x)/cos(90+x) to a single trigonometric ratio B.hence or otherwise without using a calculator,solve for X if 0<X<360. sin(x-360)sin(90-x)tan(-x)/cos(90+x) …
  9. Trigonometry

    Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 …
  10. Trig

    Solve each equation for exact solutions over the interval [0,360)where appropriate. Round approximate solutions to the nearest tenth degree. Sin^2Theta=Cos^2Theta+1 My Work: Using double angle Identity I subtract 1 to other side therefore: …

More Similar Questions