Solve the equation in the interval [0,2pi). tan(x/3) - 1 = 0.?

Question

Please list steps if you can. Thank you.

Thank you !! I was wondering why i couldnt do any of it until today, our teacher just went over it today. lol. he gave out work he shouldnt have. but thanks to all the help

Answer 1

tan(x/3) - 1 =0

tan(x/3)=1
x/3=pi/4 or pi-pi/4 or pi+pi/4
Hence
x=3 pi/4 or 3(pi-pi/4) or 3(pi+pi/4)

solution set={ 3pi/4, 9pi/4, 15pi/4}

remember: tan 45 = 1

Answer 2

let y=x/3
tan y=1
y=pi/4 or 5pi/4 but since 0 therefore y=pi/4 only since it is positive . tany is positive means y is either in 1st or 3rd quadrant. If in 3 rd quadrant then y=5pi/4 but exceed the range.
y=pi/4 is the only answer
now solve for x
x=3y=3pi/4