trig plz help

Solve, finding all solutions in the interval [0, 2π). tan(3x) = -1

asked by brittney
  1. tan (3x) = -1
    I know that 3x must be in quadrants II or IV
    and I know that tan 45° = +1 or tan π/4 = 1
    so 3x = π - π/4 OR 3x = 2π - π/4
    3x = 3π/4 or 3x = 7π/4
    x = π/4 or x = 7π/12

    now the period of tan 3x is π/3
    so adding multiples of π/3 to any answer will yield a new answer.

    x = π/4
    x = π/4 + π/3 = 7π/12 , we already have that one
    x = 7π/12 + π/3 = 11π/12
    x = 11π/12 + π/3 = 5π/4
    x = 5π/4 + π/3 = 19π/12
    x = 19π/12 + π/3 = 23π/12
    The next one will be > 2π

    So we have the above 6 solutions in the required domain.

    btw, in degrees,
    x = 45°, 105°, 165°, 225°, 285, and 345°

    check two of them:
    tan(3(105)) = -1
    tan(3(345) = -1

    posted by Reiny

Respond to this Question

First Name

Your Answer

Similar Questions

  1. Trig

    Solve the trig equation exactly over the indicated interval. tanθ = 0, all real numbers I know the answer is πn, but I don't understand how they got this. I get that tanθ = 0 on π and 2π on the unit
  2. 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
  3. math 108 trig

    1.Solve, finding all solutions in [0, 2π). cosx sin2x + sinx cosx - sinx = 0 2.Solve, finding all solutions in [0, 2π). 3sec x = 2tan^2x
  4. Precalc/Trig

    Sorry there are quite a few problems, but I just need to know if these are correct (and if they aren't, where I went wrong): 1. Solve these equations. tanθ = -√3 θ = 2π/3 + kπ θ = 5π/3 + kπ
  5. 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?
  6. Advanced Functions/Precalculus

    Trigonometry Questions 1.) Find the exaqct value of tan(11π/12) 2.) A linear trig equation involving cosx has a solution of π/6. Name three other possible solutions 3) Solve 10cosx=-7 where 0≤x≤2π
  7. calculus

    1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π? 2. what trig function never crosses the x-axis and has a value of 2 at π/6? are these correct? 3. what trig function has a
  8. Calculus

    How do I find the critical values? y= 4/x + tan(πx/8) What I did is I simplified it to y= 4x^-1 + tan(πx/8) then I took the derivative y'= -4x^-2 + (π/8)(sec(πx/8))^2 Then I simplied it y'= -4/x^2 +
  9. Trig

    can I please have help with these 3 questions? 1. Solve this equation graphically on the interval [0, 2ð]. list the solutions. sin(2x)-1=tan x 2. solve sin x cos x= sqrt3/4 3. solve tan^2 x-3tan x+2=0 thank you! show step by step
  10. Math, please help

    Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secx-cosx/secs=sin^2x 1-tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1 - 2sinx Find all solutions to the equation cosx

More Similar Questions