posted by .

Solve for all real values of x.

3tan^2x = 3^1/2 tan x

I have no idea how to approach this problem.

  • calculus -

    3^1/2 tan x *(3^1/2*tanx - 1)= 0
    tan x = 0 or 1/sqrt3

    x = 0, pi, pi/6 and one other tan^-1(1/sqrt3)

  • calculus -

    3tan^2x = 3^1/2 tan x
    3tan^2x - √3tan x = 0
    tanx(3tanx - √3) = 0
    so tanx = 0 or tanx = √3/3

    if tanx = 0, then x = 0º, 180º, 360º, ...
    if tanx = √3/3 then x = 30º, 210º,390º, ...

    The period of the tangent function is 180º, so adding 180 to any of our answers produces more answers

    the angles in radians would be
    0, pi, 2pi ...
    pi/6, 7pi/6, 13pi/6, ..
    (adding pi each time)

  • calculus -

    Much appreciated guys.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Trigonometry

    Hello, everyone: I am working on finding the exact values of angles that are less common and are therefor not found easily on the Unit Circle (at least, they are not labeled). For example, the problem I am asking about is: 10) Find …
  2. Calculus

    limit of ((1/x) - (1/|x|) as x approaches x from the left side. i have no idea how to approach this problem.
  3. Math subject Calculus

    Hi there I am having some difficulties to solve this problem from my homework package and i don't understand how to approach this problem. Please help me by giving me advice on how to approach this problem. Let z = xsin(x/y), y does …
  4. Calculus

    f(x) = [3/x^2] - [5/x^7], F(x) is the antiderivative of f(x) with F(1)=0. F(x) = ?
  5. Trig

    Solve: 3tan^2x-1=0. I got +/- (the sq. root of 3)/3 which is correct according to my study guide. However, I don't know how to use the unit circle to find this. The copy of the unit circle which I have does not have tangent values …
  6. Math

    Solve each equation for all real values of x. 7.) 3 cos 2x - 5 cos x = 1 8.) 2 sin^2 x-5 sin x + 2 = 0 9.)3 sec^2 - 4 = 0 10.) tan x (tan x-1) = 0
  7. Trig

    can I please have help with these 3 questions?
  8. Pre Calculus

    I keep trying to solve this by factring but I can't seem to get! It's so frustrating! The problem is 1+tan2x=0 This is how I worked the problem before: 1+((2tanx)/(1-tan^2x))=0 ((2tanx)/(1-tan^2x))= -1 Then I cross multiplied to get: …
  9. Tan^2 Integrals

    I'm having a hard time understanding how to do Integrals involving tan^2. I have two problems: 1. Find the integral of (tan^2 y +1)dy 2. Find the integral of (7tan^2 u +15)du 1. My approach to it is to replace the tan^2 y portion of …
  10. math-precalculus

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

More Similar Questions