Answer:
Step-by-step explanation:
same slope and same y-intercept = dependent system and represent the same line.
I'm not sure if those are words they want you use, as you didn't provide the answer choices.
![3\tan3\theta-1=0](https://tex.z-dn.net/?f=3%5Ctan3%5Ctheta-1%3D0)
![3\tan3\theta=1](https://tex.z-dn.net/?f=3%5Ctan3%5Ctheta%3D1)
![\tan3\theta=\dfrac13](https://tex.z-dn.net/?f=%5Ctan3%5Ctheta%3D%5Cdfrac13)
Recall that the tangent function has a period of
so that
![3\theta=\tan^{-1}\dfrac13+k\pi](https://tex.z-dn.net/?f=3%5Ctheta%3D%5Ctan%5E%7B-1%7D%5Cdfrac13%2Bk%5Cpi)
for any integer
. Then
![\theta=\dfrac13\tan^{-1}\dfrac13+\dfrac{k\pi}3](https://tex.z-dn.net/?f=%5Ctheta%3D%5Cdfrac13%5Ctan%5E%7B-1%7D%5Cdfrac13%2B%5Cdfrac%7Bk%5Cpi%7D3)
We get 6 solutions in the interval [0, 2π) for
,
![\theta\approx0.107](https://tex.z-dn.net/?f=%5Ctheta%5Capprox0.107)
![\theta\approx1.154](https://tex.z-dn.net/?f=%5Ctheta%5Capprox1.154)
![\theta\approx2.202](https://tex.z-dn.net/?f=%5Ctheta%5Capprox2.202)
![\theta\approx3.249](https://tex.z-dn.net/?f=%5Ctheta%5Capprox3.249)
![\theta\approx4.296](https://tex.z-dn.net/?f=%5Ctheta%5Capprox4.296)
![\theta\approx5.343](https://tex.z-dn.net/?f=%5Ctheta%5Capprox5.343)
The definition of absolute value is the magnitude of a number without the sign.
Hope this helps!
Positive 1 is the correct answer