trig

posted by .

find all values of x on interval 0-2pi.

(sin4x)(cos7x)=(cos4x)(sin7x)

identities should be used.

  • trig -

    I see use of the identity
    sin(A-B) = sinAcosB - cosAsinB

    (sin4x)(cos7x)=(cos4x)(sin7x)
    (sin4x)(cos7x) - (cos4x)(sin7x) = 0
    sin(4x - 7x) = 0
    sin (-3x) = 0
    but we know that sin(-A) = -sinA
    so
    sin(-3x) = -sin(3x)

    sin(3x) = 0
    but sinØ = 0 , Ø = 0,π,2π,3π....
    so 3x = 0, π, 2π, 3π, 4π, 5π ,6π, ...
    x = 0, π/3, 2π/3, π, 4π/3, 5π/3, and 2π

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig

    how can you confirm the identity cos^4x = (1/8)(3+ 4cos2x+ cos4x) and sin4x = (4sinxcosx)(2cos^2x-1)
  2. math(advanced algebra&trigonometry)

    the expression cos4x cos3x + sin4x sin3x is equivalent to which one of the following is the answer: 1) sinx 2) sin7x 3) cosx 4) cos7x
  3. Calculus

    Evaluate the integral e^x sin4x dx. I know the answer is 1/17 e^x sin4x - 4/17 e^x cos4x + C but I don't know how to solve it out.
  4. Math-trigonometry

    Several questions from my homework, any are appreciated. Thanks! Solve: 1) sinx-tanx=0 2) 3csc^2x=4 Find all solutions within (0,2pi) 3) cos4x(cosx-1)=0 4) cos4x-7cos2x=8 Use inverse functions where necessary to find solutions from …
  5. Trig

    cos4x*cos3x + sin4x*sin3x
  6. Pre-Calculus

    Find all solutions to the equation in the interval [0, 2pi) cos4x-cos2x=0 So,this is what i've done so far: cos4x-cos2x=0 cos2(2x)-cos2x (2cos^2(2x)-1)-(2cos^2(x)-1) No idea what to do next.
  7. Trigonometry

    Simplify the expression using trig identities: 1. (sin4x - cos4x)/(sin2x -cos2x) 2. (sinx(cotx)+cosx)/(2cotx)
  8. Math

    Can I please get some help on these questions: 1. How many solutions does the equation,2sin^2 2 θ = sin2θ have on the interval [0, 2pi]?
  9. Math (Trig)

    Rewrite the following expression in terms of tan3x: (sin2x + sin4x)/(cos2x + cos4x)
  10. Trig

    What is the period of f(x)=sin4x. I got pi/2 but on my answer list, it is not on there. a.4pi b.2pi c.pi d.1/2pi Which one would i choose?

More Similar Questions