posted by .

solve 0=(3^0.5)tan(x+(pi/6))+1 and find all general solutions

  • math -

    (3^0.5)tan(x+(pi/6))+1 = 0
    I am going to let x=pi/6 = y for easier typing

    (3^0.5)tan(y)+1 = 0

    tany = -1/√3 ...... ah!, tan 30º = +1/√3

    so y must be in the second or fourth quadrants.
    y = 150º or y = 330º or (5pi/6, 11pi/6)

    then x+pi/6 = 5pi/6
    x = 2pi/3
    x+pi/6 = 11pi/6
    x = 5pi/3

    the period of your function is pi

    so the general solutions:
    x = 2pi/3 + kpi or
    x = 5pi/3 + kpi , where k is an integer.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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) = …
  2. Math-Trig

    1. Create an algebraic expression for sin(arccosx-arcsin3x) 2. The cosx=4/5, x lies in quadrant 4. Find sin x/2 3.Determine all solutions in (0,2pie) for sin4xsin^2x=3, cot^2v(3-1)cotx=v(3), cos^2x=cosx, and tan^2x-6tanx+4=0 4. Solve; …
  3. math

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

    please help me with some questions I skipped on a review for our test coming up?

    Can someone please show me step by step solutions?
  6. Math (Pre-Calc)

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

    Solve each equation for theta, giving a general formula for all of the solutions: a. tan(theta)=-1 b. sin(theta/2)=1/2
  8. math

    Find all solutions to the equation tan(t)=1/tan (t) in the interval 0<t<2pi. Solve the equation in the interval [0, 2pi]. The answer must be a multiple of pi 2sin(t)cos(t) + sin(t) -2cos(t)-1=0 Find all solutions of the equation …
  9. Pre-Cal (Help Please!!!!)

    [Note: i need help really badly. I only have 2 hours left] Find all solutions of the following equations. Be sure to check for extraneous solutions. show work 1). 3cosθtan^(2)θ-cosθ=0 2). tan (3θ)+1=0
  10. math-precalculus

    tan^3(θ)=3tan(θ) solve for all solutions.. please provide steps so I can follow

More Similar Questions