Trig Question: solve tan(x/2+pi/3)=1 on the interval [0, 2pi]

[eh6794]

I am having a difficult time with this one.

tan(x/2+pi/3)=1 [0, 2pi]

The book says the answer is 11pi/6.

I say it is pi/6

My process:

- tan^-1(pi/4)
- x/2 + pi/3 = pi/4
- pi/4 - pi/3 = -pi/12
- -pi/12 * 2 = pi/6

 

[Deleted member 4993]

I am having a difficult time with this one.

tan(x/2+pi/3)=1 [0, 2pi]

The book says the answer is 11pi/6.

I say it is pi/6

My process:

- tan^-1(pi/4)
- x/2 + pi/3 = pi/4
- pi/4 - pi/3 = -pi/12
- -pi/12 * 2 = pi/6 ................ where did the negative sign go?!!

1 = tan^-1(π/4 ± n * π)

Continue....

 

[eh6794]

Good catch.

My answer is -pi/6

I am still not finding the book's answer

 

[eh6794]

OK. I just realized my error. -pi/6 = 11pi/6