trig plz help
posted by brittney
Solve, finding all solutions in the interval [0, 2π). tan(3x) = 1

Reiny
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
Respond to this Question
Similar Questions

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 
Trig
find all solutions to the equation √3 csc(2theta)=2 Would the answer be π/6 + 2πn, 5π/6 +2πn or π/6 + πn, 5π/6 +πn? 
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 circle, … 
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 
Math, please help
Which of the following are trigonometric identities? 
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? 
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 … 
calculus
1. what trig function has an amplitue of 1 and negative values for angles between π/2 and π? 
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 
trig
Find all solutions in the interval [0,2π) for cos(x  π/6) = 1 + cos(x + π/6). Show work, please and state in solution set.