Question

Suppose sec(0) = -6/5 and 0 is in quadrant 3. What is the value of tan(0)?

Answer 1

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:

`\begin{gathered} \tan \theta=\frac{-\sqrt[]{11}}{-5} \\ or \\ \tan \theta=\frac{\sqrt[]{11}}{5} \end{gathered}`

Therefore, the answer is:

`\tan \theta=\frac{\sqrt[]{11}}{5}`