Given the word problem, we can deduce the following information:
1. sec(θ)=-6/5 and θ is in quadrant 3.
To find the value of tan(θ), we must note first that sec(θ) = 1/cosθ. And, based on the given information sec(θ)=-6/5, the figure of it in cartessian plane should be like this:
Since cosθ=-5/6, we can determine the value of tanθ by finding the opposite side or the value of x using phytagorean theorem:
Thus, tanθ = opposite/ adjacent, it means the tanθ is:
[tex]\begin{gathered} \tan \theta=\frac{-\sqrt[]{11}}{-5} \\ or \\ \tan \theta=\frac{\sqrt[]{11}}{5} \end{gathered}[/tex]
Therefore, the answer is:
[tex]\tan \theta=\frac{\sqrt[]{11}}{5}[/tex]
