Maths

Find the nine values for x ( in radians) with 0=/< x </= 2Pi... so that sin4x = sinx ?

  1. 👍 0
  2. 👎 0
  3. 👁 216
  1. sin4x = sinx
    2sin2x cos2x = sinx
    2(2sinxcosx)(2cos^2x - 1) = sinx
    divide by sinx
    4cosx(2cos^2x - 1) = 1
    8cos^3x - 4cosx - 1 = 0

    let cosx = t

    8t^3 - 4t - 1 = 0
    using a few trials, I got t = -1/2
    and by division I got
    (2t+1)(4t^2 - 2t - 1) = 0
    t = -1/2 or t = (1+√5)/4 or t=(1-√5)/4
    cosx = -1/2 or cosx = (1+√5)/4 or cosx=(1-√5)/4
    x = 2π/3 or 4π/3 (from cosx=-1/2)
    x = .6283 or 5.6549 from cosx = (1+√5)/4
    x = 1.8850 or 4.3983 from cosx = (1-√5)/4

    in the interval 0 ≤ x < 2π there are only 6 solutions, not 9

    1. 👍 0
    2. 👎 0
  2. Should not have just divided by sinx and dropped it.

    2(2sinxcosx)(2cos^2x - 1) = sinx
    2(2sinxcosx)(2cos^2x - 1) - sinx = 0
    sinx(8cos^3x - 4cosx - 1) = 0

    so we also have sinx = 0
    x = 0, π or 2π

    the other part stays the same.
    So in addition to the 6 answers above we have these 3 new ones,
    and YES, there are 9 solutions.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc

    Use a graph to estimate the limit: lim θ->0 (sin(5θ)/θ) Note: θ is measured in radians. All angles will be in radians in this class unless otherwise specified. I tried graphing it on my calculator but the limit I got is

  2. math

    The 2 pulleys in the figure have radii of 15 cm and 8 cm, respectively. The larger pulley rotates 25 times in 36 seconds find the angular velocity of each pulley in radians per second. Find angular velocity of each pulley in

  3. Algebra

    Find all values of t such that [t] =2t+3. If you find more than one value, then list the values you find in increasing order, separated by commas. The brackets represent the floor sign function.

  4. Algebra

    Complete the table for each function. 1. f(x) = √x The x values are 0, 1,4 and 9. The corresponding y values that I got are 0, 1, 2 and 3. 2. g(x) = -1/4√ x The x values are 0, 1, 4, and 9. The corresponding y values that I

  1. Maths

    The question is "Show that z-2 is a factor of P(z)= z^3+mz^2+(3m-2)z-10m-4 for all values of m. For what values of m is (z-2)^2 a factor of P(z)?" I've proven the first part, using synthetic division, for all values of m. But the

  2. Trigonometry

    A car with wheel of radius 14 inches is moving in a speed of 55 mph.Find the angular speed of the wheel in radian per sec. your car is moving at 55 mph, which is 55*5280*12 inches/3600 seconds or 968 inches/second. each rotation

  3. Algebra 2

    Find the values of the inverse function in radians. sin^-1(0.65) a. 0.71+2pi n and -0.71+2pi n b. 0.71+2pi n and -3.85+2pi n c. 0.86+2pi n and -0.86 +2pi n d. -0.61+2pi n and 2.54+2pi n 2. tan^-1(0.09) a.-0.09+2pi n b. no such

  4. math

    The London Eye is a large ferris wheel. Each sealed and air-conditioned passenger capsule holds about 25 passengers. The diameter of the wheel is 135 m, and the wheel takes about half an hour to complete one revolution. a)

  1. Math

    Find the acute angle theta that satisfies the given equation. Give theta in both degrees and radians. cot(theta)=1/sqrt(3) The value of theta in degrees is (BLANK) degrees and in radians is (BLANK). Thank you!!

  2. math

    1.A flywheel is rotating at 7 rad/sec. It has a 15-cm diameter. What is the speed of a point on its rim, in cm/min? 2.A wheel is rotating at 3 radians/sec. The wheel has a 30 cm radius. What is the speed of a point on its rim, in

  3. Trig

    Find the coterminal angles: one positive one negative angle. 55° and (9(3.14)/5) answer degrees in radians and radians in degrees

  4. Math - Trigonometry

    For how many values of theta such that 0

You can view more similar questions or ask a new question.