Post a New Question

Trigonometry

posted by .

Solve sin 2x + sin x = 0 for 0 (Less then or equal to) x (Less then or equal to) 2pi.

  • Trigonometry -

    sin(2x)=2sin(x)cos(x)
    so
    sin(2x)+sin(x)=0
    =>
    2sin(x)cos(x)+sin(x)=0
    sin(x)[2cos(x)+1]=0
    sin(x)=0 or cos(x)=-1/2
    sin(x)=0 => x=0, x=π for 0≤x<2π
    cos(x)=-1/2 => x=2π/3 or x=4π/3

    Combining, the solution set
    S={0,2π/3,π 4π/3}
    Add x=2π if the question actually asked for
    0≤x≤2π

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Find intervals on which the following functions are increasing and decreasing. 1. f(x) = sin 2x : x is greater than or equal to 0 and less than or equal to pi 2. y = sin x + cos x [0,2pi]
  2. i lied. very quick calc problem.

    f(x) = abs(sin(x)), -pi less than or equal to x less than or equal to pi g(x) = x^2 let H(x) = g(f(x)) i got that H(x) would equal sin^2(x). THIS IS WHERE I AM STUCK! find the domain of H. do i still need to account for "-pi less than …
  3. Trigonometry

    4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant. 5. Find the exact value for cos 165degrees using the half-angle identity. 1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0 less …
  4. 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 …
  5. Math/Trig

    Solve: sin x - 2sin x cos x = 0 for 0 is less than or equal to x is less than 2pi.
  6. trigonometry

    Solve the equation 6 cos x^2+sin x=4 if 0 is less than or equal to x is less than or equal to pi
  7. Trigonometry

    Thank you STEVE!!!!! Suppose that Cos (theta) = 1/square root 2 if 0<equal to theta , pi/2 then sin(theta) = tan (theta) = If 3pi/2 less than equal to theta , 2pi then sin(theta) = tan (theta) = I know the trig functions but I feel …
  8. precalculus

    Solve sin(x) = 0.64 on 0 less than or equal to x less than 2pi There are two solutions, A and B, with A < B Give your answers accurate to 3 decimal places
  9. Trigonometry

    Solve for the following equation to the nearest degree if needed for 0 less than equal to x less than equal to 360. sin^2x=cosx 2sin^2x+cosx-cos^2x=0
  10. Pre Calc

    Solve 2 sin^2 x-3 sin x+1 =0, 0 less than or equal to x < 2pi

More Similar Questions

Post a New Question