math

Find all solutions in the interval [0,2π) that satisfy tan(x)sin²(x) = tan(x) .

  1. 👍 0
  2. 👎 0
  3. 👁 53
asked by Emma
  1. tan(x)sin²(x) = tan(x)
    tan(x)sin²(x) - tan(x) = 0
    tanx(sin² x - 1) = 0
    tanx = 0 or sin² x = 1

    if tanx = 0, x = 0, 180°, or 360° ---> x = 0,π,2π
    if sin² x = 1
    sinx = ± 1
    x = 45°, 135°, 225° or 315° ----> x = π/4, 3π/4, 5π/4, 7π/4

  2. tan ( x ) ∙ sin²( x ) = tan( x )

    Subtract tan ( x ) to both sides

    tan ( x ) ∙ sin²( x ) - tan( x ) = 0

    tan ( x ) ∙ [ sin²( x ) - 1 ] = 0

    Multiply both sides by - 1

    tan ( x ) ∙ [ 1 - sin²( x ) ] = 0

    tan ( x ) ∙ cos²( x ) = 0

    sin ( x ) / cos ∙ cos²( x ) = 0

    sin ( x ) ∙ cos ( x ) = 0

    ( 1 / 2 ) sin ( 2 x ) = 0

    Multiply both sides by 2

    sin ( 2 x ) = 0

    2 x = n ∙ π

    x = n ∙ π / 2

    n = 0 , ± 1 , ± 2 , ± 3 , ± 4...

    For n = 0

    x = 0 ∙ π / 2 = 0

    For n = 1

    x = 1 ∙ π / 2 = π / 2

    For n = 2

    x = 2 ∙ π / 2 = π

    For n = 3

    x = 3 ∙ π / 2 = 3 π / 2

    For n = 4

    x = 4 ∙ π / 2 = 2 π


    Interval [ 0 , 2 π ) is a half-open interval.

    [ 0 , 2 π ) means greater or equal than 0 and less than 2 π.

    So x = 2 π isn't solution.

    The solutions are:

    x = 0

    x = π / 2

    x = π

    x = 3 π / 2

    1. 👍 0
    2. 👎 0
    posted by Bosnian

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    find to the nearest minute, all positive values in the interval 0° ≤ θ < 180° that satisfy the equation 2 tan^2 θ - tan θ = 3

    asked by Natasha on March 7, 2012
  2. math

    find to the nearest minute, all positive values in the interval 0° ≤ θ < 180° that satisfy the equation 2 tan^2 θ - tan θ = 3

    asked by Natasha on March 7, 2012
  3. Trigonometry

    Find the exact value of tan(a-b) sin a = 4/5, -3pi/2

    asked by Dee on November 8, 2010
  4. Math (Pre-Calc)

    Find all the solutions of the equation in the interval {o,2pi) 5sqrt3 tan x+3=8sqrt3 tan x

    asked by Fiona on February 8, 2015
  5. Trigonometric

    tan^2 x − 7 tan x − 8 = 0 Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).

    asked by Diana on March 16, 2015
  6. math

    Find all solutions to the equation tan(t)=1/tan (t) in the interval 0

    asked by alicia otto on March 26, 2016
  7. trig

    please help me with some questions I skipped on a review for our test coming up? solve 5-7 on the interval 0 greater than or equal to x less than or equal to 2pi. 5. sin x=sqrt3/2 6. cos x=-1/2 7. tan x=0 ---------------- 14. what

    asked by BreAnne on February 22, 2012
  8. Solving Trig equation

    Solve the trig equation exactly in the interval 0≤x≤2π. tan x + tan π/3 ------------------ = square root 3 1 - tan x tan π/3

    asked by Anonymous on April 27, 2012
  9. math

    Solve the equation in the interval [0,2pi]. List all solutions tan^2(x)+0.8 tan(x)-3.84 = 0

    asked by applebottom on November 5, 2010
  10. Trig

    What is the total number of solutions for the equation 3 tan^2 A + tan A – 2 = 0 in the interval. 0 ≤ A ≤ π?

    asked by Kiki on March 29, 2014
  11. Integration

    Intergrate ¡ì sec^3(x) dx could anybody please check this answer. are the steps correct? thanks. = ¡ì sec x d tan x = sec x tan x - ¡ì tan x d sec x = sec x tan x - ¡ì sec x tan^2(x) dx = sec x tan x + ¡ì sec x dx - ¡ì

    asked by Vidal on October 15, 2006

More Similar Questions