Question

Take a moment to think about what tan(θ) represents.1. Use interval notation to represent the values of θ (between 0 and 2π) where tan(θ)>1.

Answer 1

Let's first get the representation of tan

We also need to understand how to convert radians to degrees

`\begin{gathered} (\pi)/(2)=90^0 \\ \pi=180^0 \\ (3\pi)/(2)=270^0 \\ 2\pi=360^0 \end{gathered}`

For question 1

since tan > 1

It must be in either first quadrant or third quadrant as shown in the diagram above

`\begin{gathered} \text{ } \\ (\pi)/(4)<\emptyset\text{ < }(\pi)/(2) \\ or\text{ } \\ (5\pi)/(4)<\phi\text{ <}(3\pi)/(2) \\ \end{gathered}`