Question

Trigonometry:

tan(theta/2 - pi/6) = 1

I'm a bit confused with how to start off on this one? considering theta is there and I don't know its value...

Answer 1

I am supposed to solve for theta, but ya know lol. Difference formula doesn't seem to apply

Answer 2

We have :
\[\tan\alpha=1\iff \alpha=\frac\pi4+2k\pi\]

Answer 3

Ooooh that seems familiar.

Answer 4

theta/2 - pi/6 = pi/4 +2kpi ?

Answer 5

I solve that?

Answer 6

exactly

Answer 7

\[\theta-\frac\pi6=\frac\pi4+2k\pi\]
So :
\[\theta=\frac\pi4+\frac\pi6+2k\pi\]

Answer 8

theta = 5pi/12 + 4kpi?

Answer 9

Wait, how did you get rid of the denominator, 2, of theta?

Answer 10

It is :
\[\frac\theta2\]
I didn't notice that !

Answer 11

Oh it is xD No problem!

Answer 12

I just don't really use the equation thing, it's a bit frustrating to me.

Answer 13

Wait, and another thing.. Isn't the period of tangent pi? not 2pi? Or am I mistaken?

Answer 14

You are right !
The period is pi !

Answer 15

Alright, well thanks for the help!