Trig

posted by .

Solve the equation in the given domain

cos 4x + cos 2x = 0, 0<(or equal to) x < pi

  • Trig -

    use the identity
    cos 2A = 2 cos^2 A - 1 on cos4A

    cos 4A = 2cos^2 2A - 1
    so
    2cos^2 2A - 1 + cos 2A = 0
    (2cos 2A -1)(cos 2A + 1) = 0
    cos 2A = 1/2 or cos 2A = -1
    2A = 60° or 300° or 2A = 180°
    A = 30° or 150° or A = 90°
    I guess I should have kept x instead of A, no big deal.
    x = 30°, 90° , 150°
    or
    x = π/6, π/2, 5π/6

    check:
    if x=30° --- cos 120° + cos 60° = -1/2 + 1/2 = 0
    if x=90 --- cos 360 + cos 180 = 1 - 1 =0
    if x = 150 -- cos 600 + cos 300 = -1/2 + 1/2 = 0

    all is good.

  • Trig -

    Thanks. Makes sense. My problem was I was trying to use another double argument property.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trigonometry

    There is an arbitrary triangle with angles A, B, and C and sides of lengths a, b, and c. Angle A is opposite side a. How do I get the formulas: b * cos C + c * cos B = a c * cos A + a * cos C = b a * cos B + b * cos A = c Are these …
  2. Math - Solving for Trig Equations

    Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360 -- cos^2x - 1 = sin^2x -- Attempt: cos^2x - 1 - sin^2x = 0 cos^2x - 1 - (1 - cos^2x) = 0 cos^2x - 1 - 1 + cos^2x = 0 2cos^2x - 2 = 0 (2cos^2x/2)= …
  3. Math - Solving Trig Equations

    Solve each equation for o is less than and/or equal to theta is less than and/or equal to 360 -- sin^2x = 1 = cos^2x -- Work: cos^2x - cos^2x = 0 0 = 0 -- Textbook Answers: 90 and 270 -- Btw, how would you isolate for cos^2x = 0?
  4. Math - Solving Trig Equations

    What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x))
  5. trig

    2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= -cos(x) 2sin(x) = …
  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. Math/trig

    Solve the equation in the given Domain: 1-cos theta/ sin theta = sqr3, 0degrees <or equal to theta < 369 degrees cos4x + cos 2x =0, 0<or equal to x < pi
  8. Precalculus

    Solve Cos^2(x)+cos(x)=cos(2x). Give exact answers within the interval [0,2π) Ive got the equation down to -cos^2(x)+cos(x)+1=0 or and it can be simplified too sin^2(x)+cos(x)=0 If you could tell me where to go from either of these …
  9. calculus

    find max, min and saddle points of the give function f(x,y)=sin(x)+sin(y)+sin(x+y) 0<=x<=pi/4 0<=y<=pi/4 i have that dz/dx=cos(x)+cos(x+y) dz/dy=cos(y)+cos(x+y) and i set them equal to zero but im kinda confused on how …
  10. Trig

    Solve each equation for the given domain. cos^2 theta + cos theta - 1 = 0 for 0-180.

More Similar Questions